Rudy Giuliani, President Donald Trump’s lawyer who has led the most extensive efforts to damage his client’s political rivals and undermine the election results, discussed with him as recently as last week the possibility of receiving a preemptive pardon before Trump leaves office, according to two people told of the discussion.

It was not clear who raised the topic. The men had also talked previously about a pardon for Giuliani, according to the people. Trump has not indicated what he will do, one of the people said.

Giuliani’s potential criminal exposure is unclear. He was under investigation as recently as this summer by federal prosecutors in Manhattan for his business dealings in Ukraine and his role in ousting the American ambassador there, a plot that was at the heart of the impeachment of Trump.

Giuliani did not respond to a message seeking comment, but after a version of this article was published online, he attacked it on Twitter and said it was false.

Christianné L. Allen, his spokeswoman, said Giuliani “cannot comment on any discussions that he has with his client.”

And Giuliani’s lawyer, Robert Costello, said, “He’s not concerned about this investigation because he didn’t do anything wrong, and that’s been our position from Day 1.”

A spokeswoman for Trump did not respond to an email seeking comment.

Such a broad pardon preempting any charge or conviction is highly unusual but does have precedent. In the most famous example, Gerald Ford pardoned Richard Nixon for all of his actions as president. George Washington pardoned plotters of the Whiskey Rebellion, shielding them from treason prosecutions. And Jimmy Carter pardoned thousands of American men who illegally avoided the draft for the Vietnam War.

Trump has wielded his clemency powers liberally in cases that resonate with him personally or for people who have a direct line to him through friends or family, while thousands of other cases await his review.

A pardon for Giuliani, who has been involved in some of the president’s most brazen acts, is certain to prompt accusations that Trump has used his pardon power to obstruct investigations and insulate himself and his allies. Andrew Weissmann, a top prosecutor for the special counsel Robert Mueller, has said that Trump’s dangling of pardons for his allies impeded their work.

In July, Trump commuted the sentence of his longtime adviser Roger Stone, who had refused to cooperate with the special counsel’s investigators and was eventually convicted of seven felonies. Last week, Trump pardoned his former national security adviser Michael Flynn, who had backed out of his cooperation agreement with the special counsel’s office for “any and all possible offenses” beyond the charge he had faced of lying to federal investigators.

The Flynn pardon raised expectations that Trump would bestow clemency on other associates — like his former campaign chairman Paul Manafort, who refused to discuss matters from the 2016 election with prosecutors — in his final weeks in office.

The president’s discussions of a pardon for Giuliani occurred as he has served as one of the loudest voices publicly pushing baseless claims of widespread election fraud that cost Trump the election. Many of Trump’s longtime aides have refused to do the president’s bidding on the election results, but Giuliani has repeatedly thrust himself into the spotlight to cast doubt on them, further ingratiating him with the president.

Giuliani has asked Trump’s campaign to pay him $20,000 a day for his work on trying to overturn the election, a figure that would make him among the most highly paid lawyers in the world. The staggering sum has stirred opposition among Trump’s aides that Giuliani has perpetuated the claims of election fraud in hopes of making as much money as possible.

Giuliani has expressed concern that any federal investigations of his conduct that appear to have been dormant under the Trump administration could be revived in a Biden administration, according to people who have spoken to him.

Legal experts say that if Trump wants to fully protect Giuliani from prosecution after he leaves office, the president would most likely have to detail what crimes he believed Giuliani had committed in the language of the pardon.

Federal prosecutors in Manhattan have been investigating since 2019 the role of Giuliani and two other associates in a wide-ranging pressure campaign directed at pushing the Ukrainian government to investigate Trump’s rivals, namely the son of Joe Biden.

The two Giuliani associates — Lev Parnas and Igor Fruman — were arrested in October 2019 as they prepared to board a flight from Washington to Frankfurt with one-way tickets. Parnas and Fruman were charged with violating campaign finance laws as part of a complex scheme to undermine the former American ambassador in Kyiv, Marie L. Yovanovitch, whom Giuliani and Trump believed should have been doing more to pressure the Ukrainians.

Prosecutors in Manhattan continued to investigate Giuliani’s role in the scheme over the past year, focusing on whether he was, in pushing to oust the American ambassador to Ukraine, essentially double dipping: working not only for Trump but also for Ukrainian officials who wanted the ambassador gone for their own reasons, according to people briefed on the matter.

It is a federal crime to try to influence the U.S. government at the request or direction of a foreign official without disclosing their involvement. Giuliani has said that he did nothing wrong and that he did not register as a foreign agent because he was acting on behalf of Trump, not any Ukrainians.