According to Alex Marvez of SiriusXM NFL Radio, Lewis is a "strong contender" for the job and may have already interviewed with Redskins owner Daniel Snyder in the Bahamas.
Lewis has served as a special adviser at Arizona State under Herm Edwards this season after spending the previous 16 years as the Bengals' head coach.
During Lewis' tenure in Cincinnati from 2003-2018, he posted a 131-122 record with four AFC North titles and seven playoff appearances. Lewis never won a playoff game with the Bengals, though, and he went just 19-28-1 with no playoff appearances in his final three seasons.
After serving as the Baltimore Ravens' defensive coordinator from 1996-2001 and winning a Super Bowl in that role, Lewis spent 2002 with the Redskins as defensive coordinator and assistant head coach before joining the Bengals.
During an interview with Zach Gelb of CBS Sports Radio in June, Lewis said he didn't miss the NFL and replied, "I don't think so" when asked if he would ever return.
A return to Washington could be attractive, though, especially with the Redskins playing much better football down the stretch this season.
Although the Redskins are just 3-12 and fired head coach Jay Gruden after a 0-5 start, they have won two of their past five games, and each of their past three losses have come by 10 points or less.
Rookie quarterback Dwayne Haskins improved significantly in recent games before suffering an ankle injury that will force him to miss Week 17, while rookie wide receiver Terry McLaurin has racked up 919 yards on the season.
Washington also has some talent on defense, including safety Landon Collins, who leads the team with 117 tackles, and pass-rushers Matthew Ioannidis, Jonathan Allen and Montez Sweat, who are all 25 or younger and have combined for 18.5 sacks this season.
Considering the fact that the NFC East champion could go 9-7 or even 8-8 this season, the Washington job could yield instant success if the young players progress and the first-round draft pick yields an impact player like Ohio State defensive end Chase Young or Alabama wide receiver Jerry Jeudy.