Lampard is in the final year of his Chelsea contract, and reports earlier this week seemed to suggest the England international is resigned to leaving the Stamford Bridge club next summer.
The 34-year-old has had 12 hugely successful years at Chelsea, winning three Premier League titles, four FA Cups and one Champions League, but the former-West Ham man has started just four league games this season.
But Wilkins, an ex-Chelsea midfielder himself, thinks Lampard can still be a useful part of the Blues squad if he accepts he may not start every game for the club.
"He's a valuable character to have around and bring off the bench," Wilkins told BBC Radio 5 Live.
"This is a 20-goals-a-season player from midfield for the last eight seasons or so, and that's a fantastic return.
"I think Frank will finally accept he is not going to play every game for Chelsea. But there is no fitter footballer for his age, probably in world football, than Frank Lampard.
"Frank plays like a 30-year-old, not a 34-year-old."
Lampard revealed earlier this month that he still feels he has two or three more years left at the highest level, and Wilkins, who coached Lampard as an assistant under Carlo Ancelotti, agrees with the England midfielder.
"I would agree with Frank's assessment that he has two or three years left at the very top level," said Wilkins. "Whether that's playing week in week out, one wouldn't think so. But most certainly he's a great asset to have around the club.
"It would be rather strange for him to finish his career at another club. In my humble opinion if I was manager of Chelsea I would want Frank to sign another contract because I know what he brings to the team and the club."