His lawyers are concerned that the president, who has a history of making false statements and contradicting himself, could be charged with lying to investigators. Their stance puts them at odds with Mr. Trump, who has said publicly and privately that he is eager to speak with Mr. Mueller as part of the investigation into possible ties between his associates and Russia’s election interference, and whether he obstructed justice.

Mr. Trump’s decision about whether to speak to prosecutors, expected in the coming weeks, will shape one of the most consequential moments of the investigation. Refusing to sit for an interview opens the possibility that Mr. Mueller will subpoena the president to testify before a grand jury, setting up a court fight that would dramatically escalate the investigation and could be decided by the Supreme Court.