The Premier League champions are looking at relegated Norwich City for some defensive depth.
The BBC's Mandeep Sanghera reports Liverpool is targeting the Canaries' Northern Ireland left-back as possible cover for Andy Robertson.
A deal for the 22-year-old Lewis would be in the £10 million range.
The native of Luton, England - who is eligible to play for Northern Ireland through his mother - made 28 appearances for Norwich this season in the league, scoring once.
Sanghera notes that the Reds could use 19-year-old Yasser Larouci as a makeweight in any deal with Larouci keen on more playing time next season. The Algeria-born Larouci made just two appearances for the Reds' first team this past season, both in the FA Cup.
Liverpool do not have a recognized left-back other than Robertson on the roster. Utility man James Milner normally spelled Robertson last season.