Mularkey told The Florida Times-Union he has put Jaguars players on notice that if they talk to the media or anyone else about the status of their injuries, he will levy $10,000 fines.
"Anything I know about a guy, anything I know is hurting on him, any comment he makes will play into how (opponents) attack a team or a position," Mularkey told the newspaper. "I just don't think it's anybody else's business."
The coach said he "will be the only voice" when it comes to information about players' injuries so as not to give opposing teams an advantage.
Mularkey's declaration, however, may prompt a fight from the NFL Players Association, a union source whose name was not reported told CBS Sports.
The broadcaster said the source indicated the union viewed the Jaguars' position as an "extreme" one that has triggered "a great deal of anger in the locker room."
An NFLPA investigation into the situation is ongoing, the report said.