The memo, from the transition team’s general counsel’s office, is the latest indication that the investigation’s special counsel, the former F.B.I. director Robert S. Mueller III, is casting a wide net in his inquiry into possible collusion between Mr. Trump’s campaign and Moscow.

The memo says former transition team members “have a duty to preserve any physical and electronic records that may be related in any way to the subject matter of the pending investigations.”

The so-called preservation order covers any transition team information involving Russia or Ukraine. It also seeks any background investigation records involving the former manager of the Trump campaign, Paul Manafort, and his business partner, Rick Gates; the former foreign policy adviser Carter Page; and the former national security adviser Michael T. Flynn. Mr. Flynn was fired for misleading Vice President Mike Pence about the nature of a call with the Russian ambassador to the United States.