On Sunday, Jason La Canfora of CBS Sports reported there's a "growing sense around the league" Jackson might succeed Lewis after being hired as a special assistant to the Bengals' head coach earlier this month. He was fired by the Browns in October.
The 53-year-old Los Angeles native, who posted an 8-8 record during a one-year stint as head coach of the Oakland Raiders in 2011, went 3-36-1 across two-plus seasons with Cleveland. That includes the team's winless 2017 season.
Jackson appeared on ESPN's First Take following his dismissal and admitted the lack of victories led to his exit from the Browns, per Pat McManamon of ESPN.com.
"Bottom line, let's just be clear, we didn't win enough," he said. "At the end of the day, when you look at it, we didn't win enough games. No matter how you cut it, regardless of what they said or how they said it, you gotta win enough games."
Jackson proceeded to lay out his vision for the future:
"I hope the next opportunity for me is to go back and be a coordinator, first and foremost. Go back and put my name back to where it should be, among some of the best playcallers in this league, and then to move forward from there. And whatever happens from there, obviously that's going to be God's decision as we move forward."
Meanwhile, Lewis, hired in 2003, is the NFL's second-longest-tenured head coach behind only Bill Belichick of the New England Patriots.
He's led the Bengals to a 130-117-3 regular-season record across 15-plus years at the helm, but the team has gone 0-7 in the playoffs under his guidance and is currently riding a two-year playoff drought.
La Canfora noted Cincinnati owner Mike Brown "almost always hires from within the Bengals family of former coaches and players." Jackson is in his third stint with the organization.
The Bengals can expect to face some fan backlash if they do decide to hire Jackson after his extreme lack of success with the team's AFC North rival.