Wolfgang Holzhauser believes a deal is already in place between the player and the west London club, while Borussia Dortmund have made a substantial bid for Kevin de Bruyne
Schurrle has been heavily linked with a summer move to Stamford Bridge and Holzhauser revealed that the German club were mulling over an offer from the Blues for the 22-year-old.
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"Andre Schurrle has probably signed a pre-contract deal with Chelsea," Holzhauser said according to Kicker magazine.
"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, which we don't have yet."
Kevin de Bruyne has been linked with a move in the other direction as a possible makeweight in a deal for Schurrle but Holzhauser believes Borussia Dortmund are pursuing the midfielder.
"He still has a few talks to hold with Chelsea," Holzhauser said of the on-loan Werder Bremen player. "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."