There will be other lawyers involved, primarily Mr. Cipollone’s two top deputies, Patrick F. Philbin and Michael M. Purpura, two people familiar with the plans said. Neither was authorized to speak publicly about the formation of the president’s defense.

Others may have discreet roles with the team, including the famed lawyer Alan Dershowitz, whose appearances on television have impressed Mr. Trump, and other members of the White House counsel’s staff.

It remains undetermined whether three of Mr. Trump’s closest allies among House Republicans — Representatives Jim Jordan of Ohio, Doug Collins of Georgia and John Ratcliffe of Texas — will play a role. They had been expected to, at Mr. Trump’s urging, until the Senate majority leader, Mitch McConnell, advised against it, according to people close to the president.