The Germany international only arrived at Stamford Bridge from RB Leipzig last July and was a regular for the Blues during the 2020-21 campaign, making 52 appearances in all competitions.
Werner scored 12 times and contributed 15 assists during his first season with Chelsea but only managed to find the back of the net on six occasions in the Premier League.
Thomas Tuchel's side are said to be keen to sign a new centre-forward this summer, with Bayern Munich's Robert Lewandowski and Borussia Dortmund's Erling Braut Haaland linked with moves, which would push the former Stuttgart youngster down the pecking order.
According to Sky Deutschland, Chelsea have made contact with a number of leading European clubs to determine whether they would be interested in signing the 25-year-old.
Werner, who still has four years left to run on his contract at Stamford Bridge, scored 95 times and contributed 40 assists in 159 appearances for Leipzig before arriving in London.