The prolific frontman has been in devastating form again for his club side this season, scoring 25 goals in 26 appearances in all competitions.
His penchant for finding the net has caught the eye of Chelsea , who are keen to bolster their attacking options.
Werner has been linked with a £60million switch to Stamford Bridge this coming summer, but it seems the 23-year-old would rather ply his trade at Liverpool.
Bild report Werner’s desire is to join up with fellow compatriot Jurgen Klopp at Anfield, who is believed to be an admirer of his talents.
Liverpool also hold strong connections with Leipzig, having negotiated with them in 2018 to secure the services of Werner’s former teammate Naby Keita.
Rumours have linked the Reds with a move for Werner in the past, but talk has gone cold in recent months.
However, as reported by Mirror Football , interest from Chelsea has put pressure on Liverpool to arrange a deal for the forward, and they are now keen to sort Werner’s transfer for the summer.
Chelsea could instead move to land Edinson Cavani on a short-term deal.
The Uruguayan forward has handed in a transfer request at PSG amid interest from Atletico Madrid.
Speaking on the 32-year-old, Blues boss Frank Lampard said: Lampard said: “He’s a great player; I played against him and I always loved his mentality and attitude, and obviously his goal-scoring record speaks for itself.
“I’m not absolutely aware of what the situation is, so we’ll see. He’s an experienced player, but so are many other players out there.
“I think we are young, and we know about the transitions. The idea of bringing in experience is something I’m certainly not absolutely looking away from.
“Because sometimes the young players need a little bit of help, and if that’s the case then that may help us.”