Special counsel Robert Mueller is seeking an interview with Mark Corallo, the former spokesman for President Donald Trump’s legal team, according to a person with knowledge of the matter, in what would be the first contact between the special counsel and a onetime member of the president’s personal legal team.

Mr. Corallo was hired last spring by Marc Kasowitz, Mr. Trump’s longtime personal attorney whom the president had initially tapped to represent him in the Mueller probe. In July, Mr. Kasowitz took on a lesser role in...