The German's current deal with the club is set to expire in the summer of 2020 which leaves Leipzig with a dilemma.
The German global is now in his third season with the club and, at just 23 years of age, has had a remarkable rise to the top of German football.
The Daily Mail claim that Liverpool, Bayern Munich and Real Madrid have all been put on alert by this claim, as they eye a move for the striker. The 23-year-old has won many admirers during his time at the club which has led to increasing speculation surrounding his future. "But he has signaled to us that he would rather not extend", the club's CEO Oliver Mintzlaff said while in conversation with Sky Sports during the half-time of their Bundesliga encounter vs Wolfsburg.
Werner scored in the game against Wolfsburg, helping Ralf Rangnick's side cruise to a 2-0 victory.
"The financial aspect will not be the decisive factor, but rather the sporting perspective".
Leipzig, missing injured top striker Yussuf Poulsen, continued to boss the midfield and launch quick attacks with Pervan making a world-class, one-handed save of a Werner shot in the 70th.
"We're trying to keep him". 13 April. Team fans are alive and this is Germany Bundesliga.
"He still has one-and-a-half years left of his contract, and I hope that he'll stay".
The Germany worldwide, who has scored 14 goals in 26 Bundesliga appearances this season, has been linked with clubs across Europe - including the Premier League leaders.