The German club’s general manager Wolfgang Holzhauser yesterday admitted the 22-year-old may have already agreed to sign for the Blues.
Holzhauser said: “Schurrle has probably signed a pre-contract deal with Chelsea. It all depends on whether we let him go. We have received a concrete offer for a fee which we are considering.
“But the price alone is not decisive. We must also have alternatives.”
Meanwhile, Bayer are plotting a bid for Chelsea midfielder Kevin de Bruyne.
Borussia Dortmund are also in the hunt for the Belgian, who has impressed on loan with Werder Bremen.
Holzhauser added: “He still has a few talks to hold with Chelsea.
“It looks like there is an offer from Dortmund to sign the player for a relatively high fee.
“According to our information, Chelsea don’t want to sell him but just loan him out.”