Trump asked his former Chief of Staff Reince Priebus about his interview with the special counsel, two people familiar with the exchange told the Times. He reportedly asked if the interviewers had been "nice" to Priebus.
In another instance, Trump told one of his aides that White House lawyer Don McGahn should publicly deny a January report alleging that McGahn told investigators that Trump had asked him to fire Mueller, the Times reported. Sources familiar with the conversation told the Times that McGahn later reminded Trump of his request.
McGahn's lawyer, William Burck, did not respond to CNBC's request for comment.
Mueller is investigating potential collusion between Trump's winning 2016 presidential campaign and Russia, along with "any matters that arose or may arise directly from the investigation."
Reports of Mueller's interest in the firing of former FBI Director James Comey, among other events, have fueled speculation that the investigation has expanded to include a potential obstruction of justice charge.
The White House did not immediately respond to CNBC's request for comment, while the special counsel's office declined comment.