The NFL Network reported Tuesday morning that trading for the former Alabama gunslinger would require "at least" a first round draft selection, according to the unnamed source.
Alternatively, Bengals.com reports that the team isn't trying to trade the quarterback.
McCarron, 26, completed 79-of-119 passes for 854 yards, six touchdowns, and two interceptions in seven games during his 2015 rookie campaign. He also started three games for injured starter Andy Dalton.
Last season McCarron didn't attempt a single throw. McCarron also has rare playoff experience. He completed 23-of-41 passes for 212 yards, one touchdown, and one interception in a start against the Pittsburgh Steelers in 2016. The Bengals lost that contest 18-16 after Chris Boswell hit a 35-yard field goal with 14 seconds remaining at Paul Brown Stadium.
McCarron is due $690,000 in 2017 on the final year of his four-year, $2.4 million rookie contract. He is a restricted free agent in 2018. He has previously been linked to the New York Jets and Cleveland Browns.
Cleveland would be an interesting fit for McCarron. Hue Jackson, the Browns' current coach, was the Bengals' offensive coordinator in 2014 and 2015. NFL sources told the Cleveland Plain Dealer that the Browns like the Bengals backup because of his familiarity with Jackson and the system.
Bengals player personnel director Duke Tobin said that the team will "listen to anyone" in trade talks.
"I'm a huge competitor. I've always been that way. I want to play," McCarron told Bengals.com. "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."