Special Counsel Robert Mueller is set to begin his interviews of current and former White House officials this week as part of his probe into Russian interference in the 2016 U.S. election, a White House official said Tuesday.

Mr. Mueller told the White House earlier this month that he may want to interview current and former officials, including communications director Hope Hicks, former Chief of Staff Reince Priebus, former press secretary Sean Spicer and White House counsel Don McGahn. The special counsel may also seek...