Special Counsel Robert Mueller’s team has interviewed former Trump campaign aide Sam Clovis and is set to interview White House Communications Director Hope Hicks next month, according to people familiar with the matter, as part of his probe of possible collusion between Trump associates and Russia in the 2016 election.

Mr. Clovis has been interviewed by members of the special counsel’s office and recently testified before Mr. Mueller’s grand jury in Washington, according to a person familiar with the matter. The person declined...