The 23-year-old is a Bundesliga sensation and has scored 70 goals in 113 games.
But after four year in Leipzig, speculation is mounting that a summer move could be on the cards.
According to The Mirror , Frank Lampard is keen on Werner.
The club legend desperately wanted a new striker through the door to ease the burden on Tammy Abraham.
However, the Blues failed to bring in either Edison Cavani or Dries Mertens - who were both on the the club’s shortlist.
Lampard looks set to face fierce competition for Werner, though.
It’s suggested Liverpool are also weighing up a bumper summer swoop.
Werner heavily hinted earlier this week that he’d welcome a Premier League move.
“What do you say if a club comes knocking in the next two weeks, a club which is one of the favourites to win the Champions League and makes an incredible offer? Most likely every player would think about it,” he told German news outlet Kicker.
“I can generally imagine playing abroad one day, although I don’t have any specific club where I want to be.
“I am open for everything. I was over in America for a holiday recently and English football was on all of the time.
“That’s an exclamation mark for the Premier League.
“But there are also big, famous clubs and it would certainly be fun playing there.”
Liverpool already have a squad bursting at the seams with superstars.
Nevertheless, former Anfield favourite Emile Heskey reckons Werner wouldn’t upset the apple cart.
“This is where your staff will have done their homework,” he told Starsport earlier this season.
“In a sense of who you bring into the club, obviously it's going to upset someone - especially when they could take your place.
“But as a player, you've got to be able to say: ‘okay I'm going to rise to the occasion’.”