The 59-year-old Lewis, with 15 years in Cincinnati, is the longest tenured head coach in Bengals history.
Lewis opted to enter 2017 -- as he sometimes did in previous seasons -- on the final year of his contract, but this time he is planning to leave Cincinnati, according to the report.
With his experience, Lewis likely will be on NFL teams' short lists of candidates after the season when multiple openings usually occur.
Most of the Bengals' assistant coaches contracts also are up as the Bengals have declined to give them extensions and some are unhappy with the way they have been treated financially, sources told ESPN.
Lewis accepted the job on Jan. 14, 2003, when the Bengals were coming off the worst season in franchise history (2-14).
Lewis has compiled a 123-111-3 record -- and 0-7 in the playoffs -- with the Bengals, who are 5-8 this season heading into Sunday's road game against the Minnesota Vikings. The Bengals won the AFC North four times under Lewis.