Giuliani said he would be be "willing to sit down with Mueller and argue it out if he has an open mind to it".
"Is the Special Counsel/Justice Department leaking my lawyers letters to the Fake News Media?"
He stressed, though, that Trump had done nothing wrong.
Senate Minority Leader Chuck Schumer said the Trump legal team's stance in their letter to Mueller is something you would see in a dictatorship.
In this May 5, 2018, file photo, Rudy Giuliani, an attorney for President Donald Trump, speaks at the Iran Freedom Convention for Human Rights and democracy in Washington.
The possibility of Mr Trump pardoning himself appeared to be raised in a January 29 letter from his lawyers to Mr Mueller, published by The New York Times on Saturday (local time), arguing Mr Trump could not have obstructed the probe given the powers granted to him by the constitution. Part of the investigation includes whether Trump tried to obstruct justice in the federal probe of Russian efforts to interfere in the 2016 US presidential election.
Statute allows him to terminate probe?
Former New Jersey Gov. Chris Christie agreed on Sunday, telling "This Week" that there is "no way" Trump will pardon himself. Many hit out at the idea of the president abusing the pardon power, while others raged at the perceived double standard employed by his personal attorney.
A special counsel is investigating Russia's role in the 2016 election, and whether Mr Trump obstructed justice. I spent a moment wondering, but in the end I think they didn't mean this the way it sounds. No president, for example, has ever tried to pardon himself.
Mueller's questions for Trump suggest that he is attempting to ascertain whether Trump obstructed justice by allegedly telling Comey that he "hoped" that Comey would let Flynn go.
Trump's lawyers and the White House had previously denied that Trump dictated the statement, declaring that Trump Jr. wrote it himself.
"I don't know how you can indict while he's in office", he added. As arguments against even asking him about the statements, they strike me as pretty silly.