Pryor suffered a concussion when hit by Broncos linebacker Wesley Woodyard, yet remained in the game for two more plays before leaving with medical staff for the locker room to be evaluated.
"It's questionable,'' a source told ESPN.
Pryor defended the job the Raiders staff did in leaving him in for two plays after the hit.
"Looked like I was functioning; I watched the tape," Pryor said. "I could definitely see why they didn't see it .... I was talking them, so I was fine because they were asking me (questions). Definitely a delayed reaction."
The union is awaiting receipt of the official game report from the Raiders before deciding how to proceed.
Raiders general manager Reggie McKenzie did not immediately return a message left on his cellphone.
NFL spokesman Brian McCarthy said all indications are that the Raiders handled the situation properly.
Pryor also said Wednesday that he believed the tackle by Woodyard was an "illegal" shot, a "helmet-to-helmet" blow.
"I think he should get fined, definitely," said Pryor, who was on his way to take a concussion test Wednesday to see if he can be cleared to practice Thursday.
Based on reviewing the game tape, the union has concerns about whether Pryor was checked for symptoms before the decision was made to allow him to continue after Woodyard's hit, and whether Pryor went to the sideline and spoke with coach Dennis Allen before the next play, as Allen says happened.
Allen said after the game that Pryor showed no immediate symptoms even though he lay face down on the field briefly after the hit. Allen stated his belief that the team followed the NFL's strict procedures.
On his Twitter account Tuesday, Pryor posted messages that indicated he had little memory of the entire game.
Sorry about the loss RaiderNation. I don't remember much ! Good hit by whoever it was. I heard our team fought well .. We will be back!
— Terrelle Pryor (@TerrellePryor) September 24, 2013
"Football's a tough sport, and there's going to be collisions and you try to do everything you can to make sure that you're taking into account player safety, and I think our medical people followed the protocol that's set forth by the NFL," Allen said.
Doctors with experience diagnosing and treating concussions have said that because of adrenaline, it is not uncommon for a player who has suffered a concussion to be unaware of the injury immediately. Doctors say a player can become symptomatic as he continues to play, that a concussion often evolves during a game following head trauma.
Information from ESPN.com's Paul Gutierrez and The Associated Press was used in this report.