The German striker is wanted by a host of top clubs, but the Reds are the favourites to sign him this summer.
And they are boosted by news that Inter Milan were recently rebuffed by RB Leipzig, per Sport.
The Italian side wanted to sign Werner, but were told no by Leipzig.
The club would want a bigger transfer fee, and they see England as the place to get it.
Werner has scored 21 goals in 25 Bundesliga games this term.
The 24-year-old wants to move to a Champions League club.