The England Under-19 striker has so far refused to sign a new contract that has been pending for 18 months.
"We haven't given him any deadline. If he stays, great. He'll be a big part of the team," manager Steve Davis told BBC Radio Stoke. "We always wanted to keep developing him. We'd welcome him being here for the next three years. That's what he's been offered."
Clayton has been at Crewe since the age of six and has represented England at Under-17 and Under-19 level.