Los Angeles (CNN) Donald Trump admitted Wednesday that he used aliases for business deals but denied that a recently-surfaced audio recording of him pretending to be his own publicist was really his own voice.

"You know, over the years I've used aliases. And when I'm in real estate and especially when I was out in Brooklyn with my father and I'd want to buy something," Trump said on ABC's "Jimmy Kimmel Live!"

"I would never want to use my name because you had to pay more money for the land. If you tried to buy land, you used different names," he said.

Asked which names he used, Trump said he liked the name "Barron," which he named his now 10-year-old son.

"I made a very good deal using that name," Trump said, without offering specifics about the deal. "I used an alias in terms of setting up a meeting with Mr. Donald Trump, and it was, and many people in the real estate business do that. You use aliases, and you have to do it. Otherwise they find out it's you, and they charge you more money and nobody wants to pay more money."

Earlier this month, Trump denied that a newly surfaced audio recording of a man sounding like Trump and posing to be his own spokesman was indeed him.

"It didn't sound like me, though, really," Trump said to Kimmel. "You think that sounded like me?"

"Yeah," Kimmel said to laughter, though the comedian praised it as a "brilliant" and "funny" tactic.

"I will say this: To me, that didn't sound like my voice," Trump said.

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Kimmel is also hosting Bernie Sanders this week, and he read out loud a question from the Democratic presidential candidate for Trump. The candidate wanted to know if he would debate Sanders and if he was prepared to talk about "major issues."

"Yes, I am," Trump fired back. "How much is he going to pay me?"

Trump went on to say that a Trump-Sanders debate "would have such high ratings" that the two could raise a lot of money for a "worthy charity."

Even if a network put up the money to host the two candidates and give the profits to a charity, Trump said, "I would love to do that."

Bernie Sanders said he was willing to do the debate on Twitter.

"Game on. I look forward to debating Donald Trump in California before the June 7 primary," he wrote.

Game on. I look forward to debating Donald Trump in California before the June 7 primary. — Bernie Sanders (@BernieSanders) May 26, 2016

Michael Briggs, a Sanders spokesman, said that Kimmel allowed the Sanders campaign to submit a question to Trump to be asked during the taping -- so they asked about a potential debate.

The Sanders campaign jokingly, but half seriously, wants to debate Trump now that Clinton has declined to debate . They think it'll be (as Trump also said) the highest rating ever on whatever network that would run it.

Briggs says that he expects that Trump will be allowed to do the same thing when Sanders tapes Kimmel Thursday night.

With Trump's attempts to revive '90's-era Clinton scandals -- and debunked conspiracy theories -- dominating headlines this week, Kimmel brought up Trump quotes from 2008 and 2012 in which the billionaire said nice things about Hillary Clinton.

Trump, as he's often done before, said that as a businessman it was smart to "speak well of everybody."

Photos: Donald Trump's rise Photos: Donald Trump's rise President-elect Donald Trump has been in the spotlight for years. From developing real estate and producing and starring in TV shows, he became a celebrity long before winning the White House. Hide Caption 1 of 37 Photos: Donald Trump's rise Trump at age 4. He was born in 1946 to Fred and Mary Trump in New York City. His father was a real estate developer. Hide Caption 2 of 37 Photos: Donald Trump's rise Trump, left, in a family photo. He was the second-youngest of five children. Hide Caption 3 of 37 Photos: Donald Trump's rise Trump, center, stands at attention during his senior year at the New York Military Academy in 1964. Hide Caption 4 of 37 Photos: Donald Trump's rise Trump, center, wears a baseball uniform at the New York Military Academy in 1964. After he graduated from the boarding school, he went to college. He started at Fordham University before transferring and later graduating from the Wharton School, the University of Pennsylvania's business school. Hide Caption 5 of 37 Photos: Donald Trump's rise Trump stands with Alfred Eisenpreis, New York's economic development administrator, in 1976 while they look at a sketch of a new 1,400-room renovation project of the Commodore Hotel. After graduating college in 1968, Trump worked with his father on developments in Queens and Brooklyn before purchasing or building multiple properties in New York and Atlantic City, New Jersey. Those properties included Trump Tower in New York and Trump Plaza and multiple casinos in Atlantic City. Hide Caption 6 of 37 Photos: Donald Trump's rise Trump attends an event to mark the start of construction of the New York Convention Center in 1979. Hide Caption 7 of 37 Photos: Donald Trump's rise Trump wears a hard hat at the Trump Tower construction site in New York in 1980. Hide Caption 8 of 37 Photos: Donald Trump's rise Trump was married to Ivana Zelnicek Trump from 1977 to 1990, when they divorced. They had three children together: Donald Jr., Ivanka and Eric. Hide Caption 9 of 37 Photos: Donald Trump's rise The Trump family, circa 1986. Hide Caption 10 of 37 Photos: Donald Trump's rise Trump uses his personal helicopter to get around New York in 1987. Hide Caption 11 of 37 Photos: Donald Trump's rise Trump stands in the atrium of the Trump Tower. Hide Caption 12 of 37 Photos: Donald Trump's rise Trump attends the opening of his new Atlantic City casino, the Taj Mahal, in 1989. Hide Caption 13 of 37 Photos: Donald Trump's rise Trump signs his second book, "Trump: Surviving at the Top," in 1990. Trump has published at least 16 other books, including "The Art of the Deal" and "The America We Deserve." Hide Caption 14 of 37 Photos: Donald Trump's rise Trump and singer Michael Jackson pose for a photo before traveling to visit Ryan White, a young child with AIDS, in 1990. Hide Caption 15 of 37 Photos: Donald Trump's rise Trump dips his second wife, Marla Maples, after the couple married in a private ceremony in New York in December 1993. The couple divorced in 1999 and had one daughter together, Tiffany. Hide Caption 16 of 37 Photos: Donald Trump's rise Trump putts a golf ball in his New York office in 1998. Hide Caption 17 of 37 Photos: Donald Trump's rise An advertisement for the television show "The Apprentice" hangs at Trump Tower in 2004. The show launched in January of that year. In January 2008, the show returned as "Celebrity Apprentice." Hide Caption 18 of 37 Photos: Donald Trump's rise A 12-inch talking Trump doll is on display at a toy store in New York in September 2004. Hide Caption 19 of 37 Photos: Donald Trump's rise Trump attends a news conference in 2005 that announced the establishment of Trump University. From 2005 until it closed in 2010, Trump University had about 10,000 people sign up for a program that promised success in real estate. Three separate lawsuits -- two class-action suits filed in California and one filed by New York's attorney general -- argued that the program was mired in fraud and deception. Trump's camp rejected the suits' claims as "baseless." And Trump has charged that the New York case against him is politically motivated. Hide Caption 20 of 37 Photos: Donald Trump's rise Trump attends the U.S. Open tennis tournament with his third wife, Melania Knauss-Trump, and their son, Barron, in 2006. Trump and Knauss married in 2005. Hide Caption 21 of 37 Photos: Donald Trump's rise Trump wrestles with "Stone Cold" Steve Austin at WrestleMania in 2007. Trump has close ties with the WWE and its CEO, Vince McMahon. Hide Caption 22 of 37 Photos: Donald Trump's rise For "The Apprentice," Trump was honored with a star on the Hollywood Walk of Fame in January 2007. Hide Caption 23 of 37 Photos: Donald Trump's rise Trump appears on the set of "The Celebrity Apprentice" with two of his children -- Donald Jr. and Ivanka -- in 2009. Hide Caption 24 of 37 Photos: Donald Trump's rise Trump poses with Miss Universe contestants in 2011. Trump had been executive producer of the Miss Universe, Miss USA and Miss Teen USA pageants since 1996. Hide Caption 25 of 37 Photos: Donald Trump's rise In 2012, Trump announces his endorsement of Republican presidential candidate Mitt Romney. Hide Caption 26 of 37 Photos: Donald Trump's rise Trump speaks in Sarasota, Florida, after accepting the Statesman of the Year Award at the Sarasota GOP dinner in August 2012. It was shortly before the Republican National Convention in nearby Tampa. Hide Caption 27 of 37 Photos: Donald Trump's rise Trump appears on stage with singer Nick Jonas and television personality Giuliana Rancic during the 2013 Miss USA pageant. Hide Caption 28 of 37 Photos: Donald Trump's rise In June 2015, during a speech from Trump Tower, Trump announced that he was running for President. He said he would give up "The Apprentice" to run. Hide Caption 29 of 37 Photos: Donald Trump's rise Trump -- flanked by U.S. Sens. Marco Rubio, left, and Ted Cruz -- speaks during a CNN debate in Miami on March 10. Trump dominated the GOP primaries and emerged as the presumptive nominee in May. Hide Caption 30 of 37 Photos: Donald Trump's rise The Trump family poses for a photo in New York in April. Hide Caption 31 of 37 Photos: Donald Trump's rise Trump speaks during a campaign event in Evansville, Indiana, on April 28. After Trump won the Indiana primary, his last two competitors dropped out of the GOP race. Hide Caption 32 of 37 Photos: Donald Trump's rise Trump delivers a speech at the Republican National Convention in July, accepting the party's nomination for President. "I have had a truly great life in business," he said. "But now, my sole and exclusive mission is to go to work for our country -- to go to work for you. It's time to deliver a victory for the American people." Hide Caption 33 of 37 Photos: Donald Trump's rise Trump faces Democratic nominee Hillary Clinton in the first presidential debate, which took place in Hempstead, New York, in September. Hide Caption 34 of 37 Photos: Donald Trump's rise Trump apologizes in a video, posted to his Twitter account in October, for vulgar and sexually aggressive remarks he made a decade ago regarding women. "I said it, I was wrong and I apologize," Trump said, referring to lewd comments he made during a previously unaired taping of "Access Hollywood." Multiple Republican leaders rescinded their endorsements of Trump after the footage was released. Hide Caption 35 of 37 Photos: Donald Trump's rise Trump walks on stage with his family after he was declared the election winner on November 9. "Ours was not a campaign, but rather, an incredible and great movement," he told his supporters in New York. Hide Caption 36 of 37 Photos: Donald Trump's rise Trump is joined by his family as he is sworn in as President on January 20. Hide Caption 37 of 37

"So when they ask me about Hillary, 'She's wonderful, her husband, everybody is wonderful,' and that's the way it is," Trump said, recalling how he would answer questions in the media.

"So you were full of shit when you said this?" Kimmel said to big laughs and applause from the audience.

Kimmel playfully introduced Trump as a "tangerine-tinted Godzilla" and "fire-breathing billionaire who incinerated all who opposed him to become his party's presumptive nominee" before he walked on set, where he got an enthusiastic reception from the crowd.

The two talked about a range of other topics, including a fundraiser in Southern California that Trump headlined Wednesday night.

Trump said some of the attendees at the fundraiser included "liberal" people, and he argued that he can do well in California this November. While previous Republican candidates haven't wanted to "waste" their time in the state, he said, Trump pledged to "make a heavy play" for the state with the most Electoral College votes, which hasn't voted Republican since 1988.

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Also in the interview, Trump did not give his personal opinion on the transgender bathroom controversy, repeating over again that it's something states should decide. Last month, Trump went against many in his own party when he said on NBC that there have been very few problems with people who "use the bathroom that they feel is appropriate."

But Trump didn't go as far on Wednesday, saying only that it's something that states should decide and refused to give his personal opinion again. He didn't say how he would vote if it were an issue on a ballot, saying only states should decide.

"I think the states will do hopefully the right thing," he said.

Asked what the "right thing" was, Trump said: "I don't know, yet. I mean I don't know."

On a lighter note, Kimmel asked Trump how he comes up with his nicknames for his opponents, like "Crooked Hillary Clinton" and "Lyin' Ted Cruz." Trump said he comes up with them himself.

Asked if he'll come up with a name for Bill Clinton, whom Trump has repeatedly dogged in recent weeks, Trump expressed no interest in creating a moniker for the former president.

"I don't want to do anything like that," he said.

Kimmel offered his own suggestion for Trump's search for a running mate, pitching the idea of hosting a "Celebrity Apprentice" where people compete to be his vice presidential pick.

"That's a good idea," Trump joked.

It was one of a few moments when Kimmel had fun roasting Trump. Before the candidate came out on set, Kimmel opened up his monologue saying the presumptive GOP nominee is within the 28 delegates needed to officially clinch the nomination.

"He's so close he can smell it like a discontinued Trump steak sizzling on the grill," Kimmel said.