According to NFL Network's Ian Rapoport, the Bengals want a first-round pick in exchange for the former Alabama signal-caller.
The 26-year-old McCarron is set to enter the final year of his rookie contract in 2017 before becoming a restricted free agent next offseason.
He is stuck behind Andy Dalton on Cincinnati's depth chart and has received limited playing time since entering the NFL as a fifth-round pick in 2014.
McCarron started three regular-season games in 2015 while Dalton was injured, going 2-1 with 854 passing yards, six touchdowns and two interceptions.
He also started in a playoff loss to the Pittsburgh Steelers that season, throwing for 212 yards, one touchdown and one pick.
In an interview with Geoff Hobson of the Bengals' official website on Monday, McCarron made it clear that he'll embrace whatever role he is placed in:
I'm a huge competitor. I've always been that way. I want to play. But it's something I can't control. There's no reason to worry about it because it spills into your life and it can affect your marriage and your relationships with people. I don't want that. A lot of people wish they could be in my shoes and get the money we to get to play a game. I love it. I'm at peace with it.
Pat Kirwan of RealFootballNetwork.com reported Tuesday that a trade involving McCarron at the draft is unlikely.
The fact that McCarron is set to become a restricted free agent means the Bengals are in line to get compensation if a team signs him to an offer sheet next offseason.
That allows the Bengals to create a high asking price, with the worst-case scenario being that they have a competent backup behind Dalton in 2017.
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