Trump raised eyebrows when he dismissed Comey, a decision he told NBC's Lester Holt was related to the Russian Federation investigation, then headed by the former director.
The Journal said the handling of the interview "could be a sign that Mr. Mueller's team doesn't view Mr. Rosenstein as a central witness in its probe, as the deputy attorney general hasn't withdrawn himself from overseeing it since that interview". The firestorm over his dismissal led to the appointment of Mueller as special counsel.
Comey was sacked in May, while he was leading the Russian Federation investigation.
CNN later confirmed that Mueller's office has interviewed Rosenstein as part of its Russian Federation probe. Special counsel investigators have been probing whether the president might have attempted to obstruct justice leading up to Comey's firing.
Rosenstein told The Associated Press in June that he would recuse from oversight of Mueller's investigation if necessary and warranted, though he has not done so as of Wednesday and it was not clear when or if he meant to.
"As the deputy attorney general has said numerous times, if there comes a time when he needs to recuse, he will".
Although, Trump did say in a July interview with The New York Times that it would be a "violation" if Mueller investigated possible financial crimes by Trump's family members or associates.
Mueller's investigation has taken several dramatic turns in recent months, in which multiple people inside and outside the Trump campaign have caught the special counsel's attention. That day, Trump met with the Russian foreign minister, Sergey Lavrov, and the Russian ambassador to the United States, Sergey Kislyak, along with other Russian officials.
"I am convinced that no matter where they end up, this investigation will run to completion even if they fire Mueller", the official said, according to the Post.
Additionally, Mueller is reportedly examining why Trump crafted a misleading statement about his son's meeting with two Russians - a lawyer and a lobbyist - at Trump Tower last June.
But Mueller's interest in the initial statement - which did not mention that Trump Jr. had been offered incriminating information on Hillary Clinton in exchange for taking the meeting, or that more than one Russian attended - has reportedly been growing as he investigates whether Trump tried to cover up any interactions he or his associates had with Russians previous year.