His pitch was reportedly introduced at a recent advisory committee meeting.
Under the proposal, coaches would be able to challenge plays flagged by an official, but coaches would not be able to challenge plays for a possible penalty if no flag is thrown.
From the report:
"You may have a questionable call during the game, but if it is not called a penalty then you can't challenge it," Mayhew said. "You don't want to have -- all of a sudden, a quarterback throws a 70-yard bomb for a touchdown late in a game or something and then you challenge it and say, 'Well, somebody was out there holding.' You don't want that.
"If they throw a flag, you can challenge it. It doesn't solve all the world's problems, but I think one of the travesties of the game -- one of the things that's going on right now that could be a lot better -- is on the Monday after the game, people are talking about the officials and the officiating and the bad calls and this call happened and that call that happened. I think they should be talking about the players on the field and what the players did in the course of the game."
In outlining the proposed change, Mayhew reportedly referenced the pivotal pass interference call that was overturned in the fourth quarter of Detroit's loss to the Dallas Cowboys in the wild-card round of the playoffs.
Mayhew reportedly said that 60 percent of the advisory committee was not in favor of the change. The competition committee will discuss the possible change in advance of the NFL's annual meeting in March.
The committee would then make recommendations regarding the rule to owners, who would vote on whether to adopt it.