It's unclear if the messages continued after Trump became president and after Mueller was appointed as special counsel in May. Strzok and the person he was texting, identified by The Washington Post as FBI veteran Lisa Page, both ended up on Mueller's team.
According to the Post, Strzok and Page were involved in a romantic relationship.
"Immediately upon learning of the allegations, the Special Counsel's Office removed Peter Strzok from the investigation," Mueller spokesman Peter Carr said in a statement Saturday. "Lisa Page completed her brief [assignment] and had returned to the FBI weeks before our office was aware of the allegations."
The inspector general's office "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," the statement said.
And on Saturday, Attorney General Jeff Sessions released a statement that he eager to "look" at inspector general's report to make sure that any Department of Justice investigation is "free from bias or favoritism."
"The allegations that the Inspector General has confirmed are part of his ongoing investigation, if proven to be true, would raise serious questions of public trust," Sessions said in the statement. "I look forward to receiving the Inspector General's report. We will ensure that anyone who works on any investigation in the Department of Justice does so objectively and free from bias or favoritism."
He added that he asked the Inspector General to complete the report "as soon as possible" because the "American people deserve answers."
Sessions concluded in the statement that he "directed that the FBI Director review the information available on this and other matters and promptly make any necessary changes to his management and investigative teams consistent with the highest professional standards.”
Meanwhile, the FBI subsequently issued its own statement on the Inspector General's inquiry on Saturday, endorsing the processes that are "designed to objectively, thoroughly and fairly determine the facts regarding potential wrongdoing."
"When the FBI first learned of the allegations, the employees involved were immediately reassigned, consistent with practices involving employee matters," the statement read. "The FBI holds all of its employees to the highest standards of integrity, independence and professionalism, as the American public rightly expects.”
Strzok has spent much of his law enforcement career working counterintelligence cases and has been unanimously praised by government officials who spoke with ABC News. He is now working for the FBI's human resources division.
He is no stranger to complex and controversial investigations.