President Donald Trump’s lawyers are seeking to determine whether special counsel Robert Mueller has an “open mind” about the Russia investigation, as they negotiate the terms of a possible interview with the president.

The legal team—which last week added former New York City Mayor Rudy Giuliani, a longtime Trump ally, and Florida attorneys Jane and Marty Raskin—met with Mr. Trump this week in Washington to discuss the strategy for negotiations with Mr. Mueller going forward, according to people familiar with the discussion.

“Does the special prosecutor really have an open mind?” Mr. Giuliani said in an interview with The Wall Street Journal. “We’re trying to assess their good faith.”

On Tuesday, Mr. Giuliani met with Mr. Mueller’s team to discuss the interview, according to another person familiar with the matter. The meeting was first reported by the Washington Post.

The former New York City mayor has known Mr. Mueller for decades, as has Ms. Raskin, who worked in the Justice Department’s Organized Crime and Racketeering Section’s Boston office in the 1980s, when Mr. Mueller served as the assistant U.S. attorney for the Justice Department’s Massachusetts office.