Washington (CNN) President Donald Trump's attorneys are trying to sway him against agreeing to an interview with special counsel Robert Mueller partially out of concern he might incriminate himself through false statements and could be charged with lying to investigators, The New York Times reported Monday evening. 
 
 The report follows on CNN's reporting last week that Trump's attorneys are arguing that Mueller's team has not met the "high threshold" it needs to have Trump in a face-to-face interview. 
 
 The Times, citing four people briefed with the matter, said Trump's attorneys want the President to refuse an extensive interview with Mueller's team and that lawyers and aides believe once refused, Mueller may not be willing to subpoena Trump in an attempt to compel a presidential interview. 
 
 Trump said last month that he wanted to speak with Mueller and would be willing to do so under oath. 
 
 "I am looking forward to it, actually," Trump told reporters. "Here is the story: There has been no collusion whatsoever. There is no obstruction whatsoever. And I am looking forward to it." 
 
 Read More ||||| CLOSE The former New York Mayor, who recently joined Trump's legal team, directly contradicted the president's claim that he had no knowledge of Michael Cohen's decision to pay Stormy Daniels $130,000. USA TODAY 
 
 President Trump and Rudy Giuliani in 2016 (Photo: Carolyn Kaster, AP) 
 
 WASHINGTON — President Trump's new lawyer is casting renewed doubt on whether Trump will sit down with Special Counsel Robert Mueller about the Russia investigation. 
 
 Attorney and former New York City mayor Rudy Giuliani said in various interviews on Fox News that the president should not be under oath, in part because of concern that prosecutors may try to lay a perjury trap for the president. 
 
 "What they’re really trying to do is trap him into perjury, and we’re not suckers,” Giuliani said Thursday on the Fox & Friends morning program. 
 
 Giuliani also questioned the need for Trump's testimony, claiming a lack of evidence that Trump had anything to do with Russians who sought to influence the 2016 election with email hacks and fake news. 
 
 “This silly deposition is about a case in which he supposedly colluded with the Russians but there’s no evidence,” Giuliani said. 
 
 The Mueller investigation has yielded indictments of more than a dozen Russians as well as former Trump associates. 
 
 Appearing on Wednesday night with Fox host Sean Hannity, Giuliani said that right now "the odds are he wouldn't be interviewed" by Mueller, but "I don't close my mind to it." 
 
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 The Mueller and Trump teams have been negotiating for more than four months on possible Trump testimony. Mueller has raised the prospect of a presidential subpoena if Trump refuses to testify, but Giuliani says the special counsel lacks the authority to enforce such a subpoena. 
 
 While most of the coverage of Giuliani's recent television interviews concerned a $130,000 Trump payment to former adult actress Stormy Daniels, the president's attorney also had has new things to say about the Mueller investigation and fired FBI Director James Comey. 
 
 When Trump fired Comey last year, he and aides said it was because of the way the former FBI director handled the Hillary Clinton email investigation during the election. Trump later said it had something to do with the Russia investigation. 
 
 On Fox, Giuliani said Trump also fired Comey because he refused to say publicly that Trump was not a target in the Russia investigation. 
 
 The attorney also called for an interview to last only two to three hours, saying that was the limit President Bill Clinton had when he testified in the Ken Starr/Monica Lewinsky case. 
 
 "I would like to get, one, not under oath," Giuliani told Hannity. "I want a videotape, not videotaped, but audiotapes, I want to make sure they don't misrepresent his answers." 
 
 Giuliani's comments reflect a more aggressive attitude by Trump legal team in the wake of a personnel shakeups. 
 
 Private attorney John Dowd left the team in March, and White House attorney Ty Cobb announced this week he will be retiring soon. Both had urged a more conciliatory approach to the special counsel. 
 
 On Fox & Friends, Giuliani said the odds of an interview became longer after the FBI raided the home and office of Trump lawyer Michael Cohen. He also blamed Mueller's office for the public revelation of a list of questions it wants to ask of Trump, though there is no evidence the Special Counsel's office leaked the document. 
 
 "Now, we are going to have some convincing to do," Giuliani said. "They’re going to have to convince us they’re going to be objective and they are not out to get us.” 
 
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– President Trump has claimed he would "love to" be interviewed under oath by special counsel Robert Mueller and that he's "looking forward" to it. His lawyers, however, are worried that Trump will make false statements, potentially leading to a charge of lying to investigators, and have urged him to turn down any interview request, the New York Times reports, citing "four people briefed on the matter." Rebuffing the interview might lead to a subpoena and a legal battle that could go all the way to the Supreme Court, but lawyers including John Dowd, who's representing Trump in the investigation, believe Mueller won't be willing to subpoena Trump and force him into a showdown, the insiders say. White House lawyer Ty Cobb supports full cooperation with Mueller's investigation, but he's outnumbered by opponents, the Times' sources say. Newt Gingrich is among those close to Trump who have publicly said that he should reject any request to be questioned. "The idea of putting Trump in a room with five or six hardened, very clever lawyers, all of whom are trying to trick him and trap him, would be a very, very bad idea," Gingrich said on Fox and Friends recently. CNN reports that Trump's team is arguing that Mueller hasn't reached the "high threshold" of evidence he would need to have Trump interviewed. (Trump has to decide whether to release a Democrat-authored memo on the Russia investigation.)