Giuliani’s Legal Bills Are Growing. His Allies Want Trump to Pay Them.

In 2019, Mr. Cohen said the Trump Organization, Mr. Trump’s family business, breached an agreement with him to cover his legal costs. In a lawsuit, Mr. Cohen said the company initially paid some of the bills after the F.B.I. searched his apartment and office in April 2018. But, he said in the lawsuit, company officials stopped the payments when they discovered around June 2018 that he was preparing to cooperate with federal investigators.

Mr. Cohen pleaded guilty later that year to charges related to tax evasion, as well as a campaign finance charge related to his 2016 hush-money payment to a pornographic film star who had claimed to have had an affair with Mr. Trump. Mr. Cohen ended up testifying about Mr. Trump in Congress, and provided assistance to the investigation led by the special counsel Robert S. Mueller III into possible conspiracy between the Trump campaign and Russian officials.

After the F.B.I. searched Mr. Cohen’s home and office, he filed a civil action against the U.S. attorney in Manhattan, which Mr. Trump joined to prevent federal officials from gaining access to material that could be protected by attorney-client privilege between Mr. Trump and Mr. Cohen.

Mr. Giuliani’s lawyers are considering filing a similar action in his case, according to one of the people close to the former mayor. One lawyer advising Mr. Giuliani, Alan Dershowitz, told CNN that it would be appropriate for Mr. Trump to join such an effort. Mr. Dershowitz confirmed the comment to The Times.

A new court filing made public on Tuesday showed the U.S. attorney’s office in Manhattan asked a federal judge last week to appoint a special master to conduct a review of potentially privileged materials seized from Mr. Giuliani.

The prosecutors, writing to Judge J. Paul Oetken, said the F.B.I. had begun to extract materials from cellphones and computers seized from Mr. Giuliani, but that a review of those materials had not yet begun, the redacted court filing showed.

Mr. Giuliani recently added four new lawyers to his team: Arthur L. Aidala, a former Brooklyn prosecutor and former Fox News commentator; Barry Kamins, a retired New York Supreme Court justice and law professor; the retired New York Appellate Division Justice John Leventhal; and Michael T. Jaccarino, a former Brooklyn prosecutor.

William K. Rashbaum, Jonah E. Bromwich and Benjamin Weiser contributed reporting.