US Special Counsel Robert Mueller, who is investigating widespread claims that Trump colluded with Russian Federation to get an edge over Hillary Clinton in the 2016 presidential election, has previously offered to allow Trump to answer his questions in writing.
"That's a no-go. That is not going happen", Giuliani told the AP.
Mueller is looking at whether the president obstructed justice in the Russian Federation investigation by firing FBI Director James Comey past year, and by criticizing his own attorney general, Jeff Sessions, who recused himself from the case in early 2017.
It's unclear if Giuliani's public position has been endorsed by Trump, who has said he wants to answer questions under oath.
Giuliani added that for now, there's "no commitment on obstruction which are post-presidential matters", but said the legal team would agree to talk "after the collusion/pre-presidential questions are over".
"It would be in written form and if you want to follow up on our answers, justify it", he said.
"We aren't going to let them spring it on us", said Giuliani, who has served as lawyer-spokesman for the president's personal legal team.
"I think we're pretty close to an agreement, maybe this weekend", he said.
Jay Sekulow, another Trump attorney, also stressed that discussions with Mueller's office are still in progress.
Despite the president's legal team's reservations, negotiations on the scope of the interview are still ongoing with Mueller's team.
If negotiations break down with Mueller, a subpoena could be issued for Trump to testify before a grand jury, which Giuliani has said they would fight all the way to the US Supreme Court.
Trump, in a Fox News interview taped ahead of a Thursday night rally in Montana, was noncommittal when asked about a possible Mueller interview. The probe's opponents slammed it as judicial overreach, and Trump himself has always been calling the entire investigation a "witch hunt". The former FBI director claimed Trump pushed him to stop a probe into Michael Flynn, who has pleaded guilty of lying to the FBI and is cooperating with the Russian investigation.