The 22-year-old left-back, who made 25 starts in the Premier League, is wanted by Jurgen Klopp, according to numerous reports.
Klopp is looking for back up for Andy Robertson and with a deal for Lloyd Kelly off the table the Northern Ireland international is understood to have agreed to sign for the champions on that understanding.
The Athletic reporter James Pearce says that Lewis is eager to get a move to Anfield and is happy to accept a understudy role to Robertson.
Lewis is believed to be desperate to learn from the likes of Robertson and Trent Alexander-Arnold. He is also represented by PLG, the management company who represent the two Liverpool stars.
Understand Jamal Lewis desperate to move to #LFC and happy to accept that he will be back-up initially. Remains to be seen whether a compromise can be reached between the clubs in terms of a fee. https://t.co/027B2Vc2A7
— James Pearce (@JamesPearceLFC) August 5, 2020
The Luton-born defender is also interesting several other clubs, who can offer the prospect of more game time.
Crystal Palace are believed to have had an offer of £12million rejected in January, while Leicester have eyed the player as a potential replacement for Ben Chilwell.
The Independent claim that Liverpool are the most advanced in negotiations for Lewis, but they have yet to agree a fee for the player.
He is under contract until 2023 and Norwich want £20m for the player, according to The Athletic.
Liverpool though value the player, who has come through the junior ranks at Carrow Road, at closer to £10m.