Mitchell, 58, is accused in the federal case of operating an illegal gambling enterprise that took in millions of dollars. He is accused of both hosting illegal high-stakes poker games at his home and illegally taking bets on sporting events.
Mitchell has pleaded not guilty.
Parmley and five other men are identified in an 84-page court affidavit as “admitted gamblers with Mitchell.”
An FBI special agent reported in the affidavit that Mitchell deposited a $1,782 check from Parmley into a bank account in 2009. The agent reported the check appears in Mitchell's records as a gambling payment.
The FBI agent describes Mitchell in the affidavit as a sports “bookie” who has been engaged in illegal gambling activity from at least 1990 to November 2010 when his wife was brutally beaten to death.
Parmley admitted to the FBI agents that he collected from Mitchell when he won bets and paid Mitchell when he lost, the source told The Oklahoman.
He told the FBI he placed his bets on the Internet.
Parmley also claimed in the FBI interview in October 2011 that he had informed TU officials he was cooperating with the investigation, the source said.
Parmley's attorney declined to comment Wednesday on that issue.
The university could face serious sanctions if the NCAA determines officials promoted Parmley to athletic director even though they knew of his gambling.
Former TU athletic director Bubba Cunningham declined to comment Wednesday. He is now athletic director at the University of North Carolina.
“As long as there is an ongoing review of whatever is going on there with the AD, he's not going to comment,” said UNC spokesman Steve Kirschner.
Cunningham left TU in mid-October 2011 for the North Carolina job. A day later, Parmley was named TU's interim athletic director and served in that position for three months before his promotion.
The turmoil at the university comes as it prepares to host the Conference USA football championship game Saturday.