The 25-year-old scored his first Premier League goal of the season in Saturday's 3-1 win over Southampton, but he has only managed two goals in eight outings in all competitions this term.
Werner has fallen down the pecking order at Stamford Bridge in terms of the centre-forward spot, meanwhile, following Romelu Lukaku's return to the club over the summer.
The Germany international started as a right-sided attacker against Southampton, but it remains unclear whether he is in head coach Thomas Tuchel's plans moving forward.
According to the Evening Standard, both Bayern and Dortmund are keeping a close eye on the situation, with the Bundesliga duo keen on signing him ahead of the 2022-23 campaign.
Werner has found the back of the net on 14 occasions in 60 appearances for the Blues since arriving from RB Leipzig in July 2020, in addition to contributing 16 assists. body check tags ::