Sources told NFL Network that the Bengals will interview Jackson as soon as Wednesday. Jackson -- who has an 11-44-1 record in four seasons as an NFL head coach -- rejoined the franchise as an assistant to coach Marvin Lewis in November.
The Browns fired Jackson on Oct. 29 after he posted a 3-36-1 record in 40 games with the franchise. The Bengals fired Lewis on Monday after he spent 16 seasons with the AFC North franchise.
Jackson, 53, began his NFL coaching career as a running backs coach with the Washington Redskins in 2001. He was promoted to the team's offensive coordinator in 2003, before joining the Bengals in 2004 as a wide receivers coach. Jackson spent three seasons in that role until becoming the Atlanta Falcons' offensive coordinator in 2007.
He spent two seasons as the Baltimore Ravens quarterback coach before becoming the offensive coordinator of the Oakland Raiders in 2010. Jackson became the Raiders' head coach in 2011 before being fired after an 8-8 campaign.
He returned to the Bengals for four seasons, serving as a secondary coach, running backs coach and offensive coordinator, before being hired in 2016 to coach the Browns.
Bengals offensive coordinator Bill Lazor and special teams coach Darrin Simmons have already been interviewed for the position. Former Denver Broncos coach Vance Joseph has also been linked to the opening and is also scheduled for an interview.
Joseph served as a Bengals assistant in 2014 and 2015. He owns an 11-21 record as an NFL head coach.