Rudy Giuliani said Wednesday that President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE's legal team has responded to special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE's latest proposal for an interview with the president, and expressed optimism the two sides could come to an agreement.

"We came back to them with a few changes, but not material changes," Giuliani, one of Trump's attorneys, said on CNN. "We are now awaiting their response."

"I'm hopeful that maybe we're going to get a yes, in which case we can probably move forward with written questions and see if that doesn't satisfy them and satisfy us," he added.

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Giuliani indicated that an interview could potentially could take place "before the election," referring to the Nov. 6 midterms.

Mueller's most recent offer to Trump's legal team included a willingness to accept some of the president's responses in writing, according to The New York Times, which added that the special counsel did not ask for written responses on the issue of obstruction.

Mueller's team and Trump's lawyers have been haggling over a potential interview with the president for months. While Trump has previously declared a willingness to speak with Mueller, his attorneys have expressed concerns that the president could perjure himself if he contradicts another witness.

Giuliani argued last month that "truth isn't truth" when explaining that Mueller could believe another witness over the president.

A forthcoming book from Watergate reporter Bob Woodward detailed an instance in January in which Trump's legal team set up a mock interview to prepare the president for a possible sit-down with Mueller.

The exercise reportedly did not go well, with Trump losing his temper after an initial round of questioning.

Trump frequently derides the Mueller investigation as a "witch hunt," and has said in recent interviews with Bloomberg News and The Daily Caller that he believes the probe is "illegal."