WASHINGTON—Special counsel Robert Mueller is investigating former White House national security adviser Mike Flynn’s work on an unfinished film financed by Turkish interests as part of its wider probe into whether Mr. Flynn improperly concealed financial ties to Turkey and to Russia, according to people familiar with the matter.

The focus on the film comes amid signs that Mr. Flynn may be working on a deal with Mr. Mueller. Mr. Flynn’s lawyers this week stopped cooperating with White House attorneys defending the president,...