Cole has recently been linked with clubs such as Manchester United, Liverpool, Arsenal and Tottenham.
The England midfielder’s contract with the Blues is set to expire at the end of June and the former West Ham star could leave the club on a free transfer.
Wilkins told BBC Radio 5 Live: “We’ve obviously been in dialogue with Joe for months now and it’s pretty evident that Carlo and myself would love Joe to stay but it’s down now to the club to see what we can do.
“We sincerely hope Joe stays with us – he’s a smashing guy and he’s a wonderful footballer so we’ll keep our fingers crossed.”
