Lawyers for President Donald Trump are increasingly skeptical of letting him give an interview with prosecutors running the Russia investigation, but are thinking through how to prepare him for the possible high-stakes session nonetheless.

Rudy Giuliani, one of the president’s outside lawyers, said in an interview Tuesday that he is currently opposed to letting Mr. Trump field questions from Special Counsel Robert Mueller. Noting the perils of talking to prosecutors, Mr. Giuliani said that were the president to testify he...