Werner enjoyed a fantastic breakout campaign for RB Leipzig last season after joining from Stuttgart for just £8m, scoring 21 goals in 31 games.
The 21-year-old German international, who has already scored six goals in 9 games in all competitions this season, is reportedly being tracked by both Barcelona and Real Madrid.
According to the aforementioned source, both clubs see Werner as a viable option to boost their strike forces which require additions after the transfer window.
Barca sporting director Robert Fernandes has reportedly been tracking the RB Leipzig striker for a while and has been watching him play for the Bundesliga side this season, and the Catalan club are looking for an upgrade on Paco Alcacer, who has failed to convince since his move from Valencia last summer.
Meanwhile, Real Madrid are yet to find a replacement for Alvaro Morata, who made the £70m move to Chelsea in the summer.
Both clubs are said to be even more attarcted to the German forward given that he does not have a mammoth release clause in his contract.
Although Werner has said he is happy at Leipizg, and his contract runs until 2020, the striker has admitted he would like to fulfill a dream of joining a bigger club.