Sassuolo chief Giovanni Carnevali admitted he would consider bids for Domenico Berardi from Chelsea, but only if they are presented soon.
As quoted by Gazzetta dello Sport, Carnevali explained he would not be accepting offers for his players past early August.
Manuel Locatelli is the main source of transfer speculation, with Arsenal and Juventus jostling for his signature.
“We are waiting for an adequate offer, otherwise Locatelli will remain at Sassuolo,” said Sassulo’s man in command.
“In early August we will close our market.”
Shutting the Italian’s exit door could also potentially affect Berardi.
Chelsea recently emerged as reported admirers of the 26-year-old, alongside Liverpool and Borussia Dortmund.
Although he has two years left on his contract, Carnevali said the right proposal could sway him to sell the exciting winger.
He told Sky Sports Italia: “Berardi is our flag; the will is to continue with him because he represents us.
“But if an important offer comes in this case too for us and for the boy, we would rate it, but the desire is to continue with him.”
Berardi bagged 17 goals last season and was part of Italy’s European Championship-winning squad.
Gazzetta dello Sport quoted an asking price of €50m (£43m) from Sassuolo for his services.
Chelsea currently have their eye on other attacking options but are running out of time to secure any new signings.
Landing Berardi would seemingly not go down well with Blues supporters.
Thomas Tuchel has enough creative talent to contend with already; what he wants is an efficient no.9.