Cole believes Rooney still has unfinished business at Old Trafford.
"His days here are not over - far, far from it," Cole told the Manchester Evening News.
"He is a young man and the best years are still in front of him. No way has he peaked.
"The only two people you could get an answer from about why his season was what it was is Sir Alex and Wayne Rooney.
"But whatever has happened I still think going forward it is important to keep Wayne Rooney at United because he is a top player. It is important for Manchester United to keep every top player at the club.
"Hopefully he will stay. I love watching him play. He plays with great endeavour and great energy."