Special Counsel Robert Mueller’s office is exploring whether longtime Trump adviser Roger Stone tried to intimidate and discredit a witness who is contradicting Mr. Stone’s version of events about his contacts with WikiLeaks, according to people who have spoken to Mr. Mueller’s investigators.

In grand jury sessions and interviews, prosecutors have repeatedly asked about emails, text messages and online posts involving Mr. Stone and his former friend, New York radio personality Randy Credico, the people said. Mr. Stone has...