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 asserted that Mr. Credico was his backchannel to WikiLeaks, a controversial transparency group, an assertion Mr. Credico denies.

Mr. Mueller’s investigators are probing whether Mr. Stone had direct contact with WikiLeaks and knew ahead of time about its release of stolen Democratic emails, as he claimed during the campaign and now denies. Mr. Stone says he is angry at Mr. Credico because his ex-friend has “refused to tell the truth” about being his conduit to WikiLeaks.

Filmmaker David Lugo, who knows both men, said in an interview he has testified before Mr. Mueller’s grand jury about a blog post Mr. Stone helped him draft that was harshly critical of Mr. Credico. Another witness, businessman Bill Samuels, said he was questioned by Mr. Mueller’s team about Mr. Credico’s reaction to allegedly threatening messages sent by Mr. Stone.

Prosecutors also are examining messages between Messrs. Stone and Credico that involve the radio personality’s decision to assert his Fifth Amendment before Congress, according to a person familiar with the probe.