He registered 12 goals and 15 assists from 51 appearances last term but was still disappointing with multiple scoring chances missed.
A recent report claimed that Werner is considering his Blues future and could leave the club if they sign a new striker this summer.
It was suggested that he would prefer a return to the Bundesliga, and Bayern have now been credited with fresh interest in signing him.
The club are eyeing a long-term successor for Robert Lewandowski, and manager Julian Nagelsmann is keen on a reunion with Werner.
Werner was poor with his finishing in his debut campaign, and this has urged the Blues to pursue another elite striker this summer.
The 25-year-old can also play out wide, but the vast share of his success in his career has come through leading the line.
His playing time could be hampered with a new striker signing. It won’t come as a surprise if he leaves the Blues after one season.
Bayern are long-term admirers of Werner, and their chances of signing him could be boosted by the presence of Nagelsmann.
Nagelsmann managed Werner at Leipzig for just one season (2019/2020). He got the best out of him with a stunning tally of 34 goals and 13 assists from 45 games.
Werner regularly played in a front two. He could form a fearsome partnership with Lewandowski next term if he can revive his form.
Werner has four years left on his Blues contract. He is valued at €65m by Transfermarkt, and the club may look to make a quick profit on him.
Stats from Transfermarkt.com