BILD says the Germany international favours a switch to Liverpool over all other offers.
Werner penned a new deal with RBL to 2023 last year, however it's a contract that carries a buyout clause set at €55-60m. The clause must be triggered by the end of April before it becomes void.
The only question is whether Werner wants to leave Leipzig this summer. However if the does, it will be Merseyside where he plans to go.
After victory at Champions League opponents Tottenham this week, matchwinner Werner stated: "I know that Liverpool is the best team at the moment in the world and when you are linked with that team it makes me very proud.
"It's a pleasure but I know that Liverpool play a lot of good players and I have to improve myself and I need to learn many more things to get to that level and to play there."