A lawyer who previously advised Michael Cohen, the key government witness in the hush money payment investigation into President Trump, has been invited to appear Monday before a Manhattan grand jury that is considering potential charges against the former president, according to a person familiar with the matter.

Robert Costello had advised Cohen before the two had a falling out, and is prepared to offer testimony to the grand jury attacking the credibility of Cohen’s statements, according to the person, who insisted on anonymity to discuss secret legal proceedings.

Mr. Costello had contacted a lawyer for Mr. Trump saying that he had information that contradicted Cohen’s current statements and that could be exculpatory for Mr. Trump, the person said. The lawyer brought it to the attention of the district attorney’s office, which last week subpoenaed Mr. Costello’s law firm for records and invited him to provide testimony on Monday afternoon.

The Manhattan district attorney’s office declined to comment on Sunday. Prosecutors have not said when they expect to conclude their work or when or if Mr. Trump might be charged. The former president claimed in a post on Saturday that he would be arrested on Tuesday, though people close to him later said that he had been given no updates from prosecutors.

Cohen is a former lawyer and fixer for Mr. Trump who has been a key witness in District Attorney Alvin Bragg’s investigation, meeting regularly with prosecutors and appearing before the grand jury earlier this month.

Cohen served prison time after pleading guilty in 2018 to federal charges, including campaign finance violations, for arranging the payouts to porn actor Stormy Daniels and model Karen McDougal to keep them from going public. Mr. Trump has denied the affairs.

Mr. Costello is a veteran New York lawyer who has represented Trump allies including his adviser Steve Bannon and his personal lawyer Rudy Giuliani. Mr. Costello’s connection to Cohen was highlighted in the report of special counsel Robert Mueller, who investigated links between Russia and Trump’s 2016 presidential campaign as well as efforts to obstruct the probe.

According to the Mueller report, Cohen began speaking with Mr. Costello in April 2018, days after the FBI raided Cohen’s home, hotel room and office. Amid public speculation about whether Cohen would begin cooperating with investigators, Mr. Costello emailed Cohen to reassure him that he had had a “Very Very Positive” conversation with Mr. Giuliani and that “you have friends in high places.”

Cohen has waived his attorney-client privilege with Mr. Costello, which would allow him to describe their conversations, the person said.

Mr. Bragg signaled over the weekend that he is standing firm against Mr. Trump’s increasingly hostile rhetoric against, telling his staff that the office won’t be intimidated or deterred as it nears a decision on charging the former president.

Mr. Bragg sent an internal memo late Saturday hours after Trump unleashed a three-part, all-caps social media post in which he said he could be arrested in the coming days, criticized the district attorney and encouraged his supporters to protest and “TAKE OUR NATION BACK!”

The memo came as law enforcement officials in New York City are making security preparations for the possibility Mr. Trump is charged and appears in court in Manhattan.

“We do not tolerate attempts to intimidate our office or threaten the rule of law in New York,” Mr. Bragg wrote, referring to “press attention and public comments” regarding an ongoing investigation by his office.

As Mr. Bragg sought to assuage concerns about potential threats, posts about protests began popping up online, including a rally on Monday against Mr. Bragg organized by the New York Young Republican Club.

Law enforcement officials in New York are also closely monitoring online chatter warning of protests and violence if Mr. Trump is arrested, four law enforcement officials told The Associated Press. The threats that law enforcement agents are tracking vary in specificity and credibility, the officials said. Mainly posted online and in chat groups, the messages have included calls for armed protesters to block law enforcement officers and attempt to stop any potential arrest, the officials said.

The law enforcement officials are also discussing a multitude of security plans for lower Manhattan in the event Mr. Trump is indicted. Those plans — which the officials described as preliminary — include the potential for closing down several streets around the Manhattan criminal courthouse and blocking streets with large trucks, similar to security protocols in place for major events and parades in New York.

In a post Sunday, Mr. Trump lambasted Mr. Bragg — Manhattan’s first Black district attorney — as a “Racist in Reverse,” and accused him of taking orders from the Justice Department and being a pawn for billionaire Democratic donor George Soros, who supported Mr. Bragg’s campaign through the Color Of Change PAC.