Manager Jurgen Klopp has earmarked the Canaries defender as the ideal deputy for Andy Robertson on the left side of his defence with the 22-year-old impressing during his maiden season in the Premier League last term.
It was revealed earlier this week that Lewis was on the Reds’ radar with the Premier League champions willing to go to around £10m for the Northern Ireland international.
Norwich are hoping to get around £20million for one of their stars of last season with negotiations expected to continue with the premier league champions.
The Reds were hoping a substantial sell-on clause would be enough to see the club’s sporting director, Stuart Webber, accept the initial offer.
Liverpool were mindful that Lewis’s status as backup to Scotland captain Robertson could prove a sticking point in making the premier agree to a move.
Lewis is eager to work with Klopp after seeing him turn Liverpool from a mid-table side upon his arrival in October 2015 to one that is the current world, European and English champions.
With Lewis’s heart set on a move to Anfield this summer, the Reds feel they will eventually see Norwich do business as Daniel Farke begins the rebuild following their relegation from the top flight last term.