President Trump drew criticism for his apparent acceptance of Russian President Vladimir Putin's denials of election meddling.
The Post reported that Strzok and Page exchanged texts that were anti-Trump and pro-Clinton.
A lawyer for Storzok declined to comment.
The Justice Department 's Office of the Inspector General said in a statement Saturday that it has been "reviewing allegations involving communications between certain individuals, and will report its findings regarding those allegations promptly upon completion of the review of them".
At the time they left Mueller's group, no one publicly linked the two departures.
Mr Flynn pleaded guilty on Friday to lying to the FBI and agreed to co-operate with Robert Mueller's investigation.
Lisa Page, an FBI lawyer who was assigned to the Mueller investigation, received the messages.
Strzok's return to an FBI post in the human resources division was cast as a promotion by some at the bureau, despite the fact it is widely seen to be a demotion. Word of the texts could give new fuel to those demands.
He was the FBI's lead investigator on the Clinton email investigation, so much so that he interviewed the former secretary of state on July 2, 2016.
"Immediately upon learning of the allegations, the Special Counsel's Office removed Peter Strzok from the investigation", said Peter Carr, a spokesman for the special counsel's office.
By hiding from Congress, and from the American people, documented political bias by a key FBI head investigator for both the Russian Federation collusion probe and the Clinton email investigation, the FBI and DOJ engaged in a willful attempt to thwart Congress' constitutional oversight responsibility.
McCabe, the deputy director, has faced repeated questions from the White House and Republican lawmakers about whether he should have been involved in the Clinton case at all - given the hundreds of thousands of dollars in political donations made to his wife, a candidate for political office in Virginia, by a key Clinton ally in 2015.