Mr Giuliani underscored one of the main arguments in a newly unveiled letter sent by Mr Trump's lawyers to Mr Mueller back in January: A president can not be given a grand jury subpoena as part of the investigation into foreign meddling in the 2016 election.
"I mean, we're leaning toward not", Giuliani told ABC.
A 20-page memo sent to Mueller by Trump's attorneys John Dowd and Jay Sekulow in January and published in full by The New York Times last week argues that Trump can not be guilty of obstruction of justice because he has full jurisdiction over all federal investigations.
Sanders again professed the president's innocence when she was asked about another Trump tweet that declared Mueller's investigation "totally UNCONSTITUTIONAL!"
The dispute among scholars on the issue nearly guarantees that if Trump faced indictment and pardoned himself, the next step would be a court challenge, with the President's fate decided by judges - or even the Supreme Court.
Nevertheless, Trump's lawyers are "trying to come up with a narrow group of conditions in which" Trump could testify before Mueller's team, "if we can justify the fact that they have an open mind and that they'll conclude the investigation".
Last year Trump had said that he has the "complete power to pardon".
"If the President decided he was going to pardon himself, that's nearly self-executing impeachment".
"This is from a letter from the outside counsel, and I direct you to them to answer that question", Sanders told reporters regarding the letter at a press briefing Monday.
The issue was just one of several relating the special counsel's investigation and the handling of it by the President's personal attorneys.
The former FBI Director, Mueller, is now carrying investigations into the alleged interference of Russian Federation in the 2016 presidential elections.
The White House and a spokesperson on the special counsel refused to comment.
If Mr. Trump does not consent to an interview, Mueller will have to decide whether to go forward with a historic grand jury subpoena. "This is a power left to presidents without limitation beyond barring its use to effectively block an impeachment".