WASHINGTON — Rudy Giuliani, whose advocacy of a debunked conspiracy theory ultimately led to President Donald Trump’s impeachment, is lobbying to join the president’s defense team in the Senate trial but has so far been rebuffed.

Giuliani, who has acted as Trump’s attorney for free since early 2018, has been “working Trump hard” to be included among the lawyers who will defend him on the floor of the Senate, according to an informal adviser close to the White House who spoke on condition of anonymity.

The White House declined to comment on Giuliani. A second informal adviser said Giuliani has not really been aggressively lobbying, but has made it known that he is “available” to offer his services. “They said, ‘Thanks, but no thanks,’” the adviser said, also on condition of anonymity.

Giuliani did not respond to HuffPost’s queries on the matter.

The former New York City mayor has, however, made it clear in recent public statements that he would enjoy arguing Trump’s case before the Senate. “I’d try the case. I’d love to try the case,” Giuliani told reporters at Trump’s New Year’s Eve party for paying guests at his Palm Beach resort. “I don’t know if anybody would have the courage to give me the case. But if you give me the case, I will prosecute it as a racketeering case.”

And Saturday night, Giuliani told Fox News host Jeanine Pirro he would ask for the U.S. Supreme Court to dismiss the case against Trump, which, in his view, would have the effect of expunging the impeachment from Trump’s record. “I would say if it’s nonconstitutional, it’s null and void,” he said.

Trump responded by posting a tweet of the interview with the statement: “Thank you Rudy!”

Top White House aide Kellyanne Conway told reporters Friday that Trump’s case would be handled by White House counsel Pat Cipollone, his two deputies and Jay Sekulow, another of Trump’s personal lawyers. She was noncommittal on the possibility of any others joining the team.

JIM WATSON via Getty Images “I’d try the case. I’d love to try the case,” Rudy Giuliani told reporters of President Trump's Senate impeachment trial.

Giuliani, a onetime federal prosecutor, bought into the false story that Russia had not helped Trump win the 2016 election, but rather it was Ukraine framing Russia with fake evidence. Giuliani was making that story a centerpiece of his planned rebuttal to special counsel Robert Mueller’s report.

Mueller found last spring that Trump’s campaign had expected and welcomed election help from Russia but did not engage in a criminal conspiracy to obtain it. The special counsel did not recommend any specific actions by Congress against Trump, and the White House never released Giuliani’s response.

Giuliani nonetheless continued pushing the theory to Trump — particularly the element that former Vice President Joe Biden’s son Hunter Biden had somehow been involved and that an investigation into the younger Biden’s job with a Ukrainian energy company could hurt his father’s campaign for the Democratic presidential nomination. Last spring, Trump and his top advisers believed Biden presented the most potent threat against Trump’s reelection.

According to testimony by State Department and National Security Council officials during impeachment proceedings in the House, Trump responded by referring them to Giuliani when questions arose about his Ukraine policy.

“Go talk to Rudy,” recalled Gordon Sondland, the U.S. ambassador to the European Union who had become Trump’s point person in charge of Ukraine after the president, at Giuliani’s urging, recalled the ambassador to Ukraine back to Washington.

Trump even personally referred the new Ukrainian president to Giuliani in their July 25 phone call. “I will have Mr. Giuliani give you a call,” Trump said, according to a rough transcript released by the White House. “Rudy very much knows what’s happening, and he is a very capable guy. If you could speak to him that would be great.”

Trump was impeached last month for trying to coerce Ukrainian President Volodymyr Zelensky into opening investigations into the Bidens and the election conspiracy theory, using $391 million in congressionally approved military aid to Ukraine as leverage. Trump had ordered the aid withheld but released it after learning that a whistleblower had filed a formal complaint about his conduct and that it was likely to reach Congress.

Trump’s upcoming trial for abuse of power and obstruction of Congress notwithstanding, he has continued to push the conspiracy theory — a theory so convoluted that conservative radio host Glenn Beck needed two chalkboards to explain it all.

Former NSC staffer Fiona Hill testified during the impeachment proceedings that the conspiracy theory was actually Russian disinformation designed to obscure the country’s responsibility for helping Trump win. “This is a fictional narrative that has been perpetrated and propagated by the Russian security services themselves,” she said.

Trump’s own former homeland security adviser, Tom Bossert, called the theory baseless in an interview with ABC News. “It’s not only a conspiracy theory, it is completely debunked,” he said in September. “I don’t want to be glib about this matter, but last year, retired former Senator Judd Gregg wrote in The Hill magazine Five Ways or Three Ways to Impeach Oneself and the third way was to hire Rudy Giuliani.”