Ian Rapoport of the NFL Network reported the news.
ESPN's Dianna Russini provided further details ahead of the trade deadline next Tuesday:
Dianna Russini @diannaESPN
Bengals told Carlos Dunlap not to come to practice today. (@RapSheet first) Source tells me it’s been “a little crazy there” between the pass rusher and the coaching staff. The team is discussing moving him before the trade deadline. Told we will all know more later #Bengals
Dunlap has been one of the league's most consistently effective edge-rushers since the Bengals selected him in the second round of the 2010 draft.
The 31-year-old University of Florida product ranks 10th among active players with 82.5 career sacks, per The Football Database. He's also recorded at least 7.5 sacks in seven straight seasons, including a career-high 13.5 quarterback takedowns in 2015.
He's off to a slow start this season, however, with one sack through seven appearances.
"The tape, I'm told, shows a guy who isn't just playing poorly, but is playing like he doesn't care. Which, ultimately, won't help the Bengals trade him," Albert Breer of Sports Illustrated wrote Monday.
Dunlap is signed through 2021 as part of a three-year, $40.65 million contract that includes a $13.5 million salary-cap hit next season, per Spotrac. That could also complicate trade talks.
He voiced his frustration on social media last week, writing "I don't got time for this" in a later-deleted Instagram post (via SI's James Rapien) after being listed third on the depth chart.
Dunlap, a two-time Pro Bowl selection, would be a major addition for a team seeking pass-rushing help if he can return to form outside Cincinnati.
The Bengals will likely struggle to get anything substantial in return given his contract, the drop in production and the drama that's surrounded him in recent weeks, though.