Investigators inside the office of Special Counsel Robert Mueller reacted with a mixture of skepticism and laughter at Rudy Giuliani’s claim that he will negotiate a swift end to Mueller’s probe of President Donald Trump and his alleged involvement in possible Russian election meddling and obstruction of justice, FOX Business has learned.

Giuliani, the latest addition to the president’s legal team, has stated both to associates and to reporters in recent days that he will be reaching out to Mueller with the intention of ending the probe into Trump’s conduct and that he will achieve this goal in a matter of weeks, according to people with direct knowledge of the situation.

As the former New York City mayor’s remarks made their way to Mueller’s investigators, they were said to be “amused,” according to one person with direct knowledge of the matter. Mueller’s team has signaled that its probe of Russia’s possible meddling in the 2016 presidential election is exploring new avenues presented by at least two cooperating witnesses and that there is little Giuliani can do to force Mueller’s hand, these people add.

“If Rudy comes to Mueller trying to negotiate anything short of a presidential guilty plea, he will likely be met by deaf ears,” said a lawyer who follows the case from Washington.

A spokeswoman for Giuliani hadn’t return calls and email messages requesting comment. A spokesman for the special prosecutor declined to comment.

“Giuliani’s great, but I don’t think he’s going to move the dial one way or another,” Chris Swecker, a white-collar criminal attorney and former assistant director of the Federal Bureau of Investigation, said in an interview with Neil Cavuto on FOX Business. “I know how Mueller operates. He’s not going to let anyone stampede him into it early or bring this case to an early conclusion.”

Swecker, however, did say he believes the Mueller investigation is coming to a conclusion.

“I do think something’s going to happen in the next month or two,” Swecker said.

Mueller has put off the sentencing until later this month of two former Trump aides charged in the Mueller probe: Former National Security Adviser Michael Flynn and former campaign aide George Papadopoulos.

“This leads me to believe he is keeping his witnesses on ice until the next indictment,” Swecker added. “Working your way up the food chain to the next level … related to Russia collusion … I don’t think the president is going to get brought into this, but I do think there is something else coming.”

Swecker cited as possible targets of criminal prosecution Donald Trump Jr., the president’s son who met with Russian operatives promising compromising information on Hillary Clinton, his father’s Democratic opponent during the 2016 campaign, and Jared Kushner, the president’s son-in-law and currently a White House adviser, who also appeared at that meeting.

Both Donald Trump Jr. and Kushner have said they’ve done nothing wrong; the president has repeatedly called the probe a “witch hunt.”

If members of the Trump inner circle conspired with Russian operatives to sway the election – even if the conspiracy was fruitless – that would form the basis for a federal indictment of them and could lead to the impeachment of the president himself. Mueller was appointed special prosecutor after Trump fired James Comey as FBI director last year; Comey had been heading the inquiry into Russian collusion.

The year-long investigation has produced several indictments of Trump aides, but for crimes that have little to do with possible Russian meddling, or even obstruction of justice, another area Mueller is investigating as an outgrowth of the Comey firing. Trump’s legal team, meanwhile, is in turmoil. His lead attorney, John Dowd, recently resigned after finding it difficult to work for the volatile president, who didn’t heed his advice. Dowd is the only lawyer on the Trump team who examined every document the White House surrendered to Mueller, according to a personal familiar with the situation. Trump has faced rejections by a number of high-powered litigators to join the team.

“He hasn’t seen a courtroom in 30 years, except for his divorces and a stint as juror.” - –White-collar attorney

But with the addition of Giuliani, the former New York City mayor and famed prosecutor of mob and Wall Street transgressions when he was U.S. attorney for the Southern District in the 1980s, Trump may be able to regain momentum. Giuliani is well known in legal circles and has become a staunch supporter of the president. He is also said to have a good relationship with Mueller, with whom he worked at the Justice Department. He will be joined by two other former prosecutors to help with ending the probe: Jane and Marty Raskin.

Still, legal experts were skeptical about Giuliani’s immediate impact.

“He hasn’t seen a courtroom in 30 years, except for his divorces and a stint as juror,” one white-collar attorney said.

It’s difficult to gauge just where Mueller is going in his probe. Bloomberg reported on Thursday that Deputy Attorney General Rod Rosenstein alerted the president that he wasn’t a target of the investigation – a positive sign for Trump that caused the Dow Jones Industrial Average to pare its decline for the day. Trump had been threatening to fire Rosenstein, the Justice Department’s point man on the Mueller inquiry, for giving the special prosecutor too much leeway in prosecuting crimes that fall outside of possible Russian meddling.

But legal experts said such classifications mean little because Trump is already a subject of a probe and could immediately become a target based on new evidence. Recently, the offices of Michael Cohen, Trump’s personal lawyer, were raided after a referral from the Mueller team to New York federal prosecutors, a move that angered the president. Cohen hasn’t been charged but was under surveillance while representing Trump and remains under investigation by the U.S. attorney for the Southern District.

Cohen's attorney declined to comment.