Per that report, "With a flurry of head coaching openings expected in the coming weeks and a shortage of obvious head coaching candidates with experience, Lewis is likely to be on teams' short lists of candidates."
He also reportedly would be interested in taking on an advisory role for one of his former assistant coaches, such as Minnesota Vikings head coach Mike Zimmer.
Both Schefter and Ian Rapoport of NFL.com reported Lewis could seek a front-office position, such as general manager, as his next job. Rapoport offered more details on both Lewis' and the Bengals' future:
Schefter also reported Lewis' coaching staff could be on the way out as well:
"Not only is Lewis' contract up, but so are those of most, if not all, of the Bengals' assistant coaches. The Bengals have declined to give contract extensions to their assistant coaches, and some are unhappy with the way they have been treated financially, sources said.
"Amid the uncertainty and potential change, the Bengals are likely to undergo a major overhaul to their coaching staff. Some assistants could wind up staying, but many are expected to leave along with Lewis."
With Lewis' contract up after the season, his coaching staff reportedly unhappy with the organization and the 5-9 Bengals struggling, the writing is on the wall.
Nate Davis of USA Today ranked Lewis No. 1 in his NFL hot-seat rankings this past week, noting "Cincy's briefly flickering playoff hopes are now permanently doused, and it's all but inevitable that Lewis is finishing out his contract with no hope for another one."
Nonetheless, Paul Dehner Jr. of the Cincinnati Enquirer reported the Bengals were "caught off guard" by Sunday's news.
Lewis, 59, has spent 15 seasons as the Bengals head coach, accumulating a 123-112-3 record while leading the team to the postseason seven times.
Lewis' tenure in Cincinnati may be ending on a down note, but as Field Yates of ESPN noted, he helped turn around a franchise that hadn't made the playoffs in 14 straight seasons before Lewis led them there in 2005:
He was also the most successful coach in Bengals history by a wide margin, at least from a statistical perspective, per ESPN Stats & Info: