The Blues manager expresses his hope that the England left-back signs a new contract with the European champions but understands that the board will make the final decision
The left back's current deal expires in the summer, but he is subject to club owner Roman Abramovich's contract extension policy, which only permits offers of a one-year extension to players older than 30 - a main reason why Dider Drogba left the London club at the end of last season.
Foreign sides will be able to offer Cole pre-contract proposals from January and officially sign him once his time with Chelsea is over, meaning that the Blues' board only have around two months to agree on a new deal with Cole.
"My recommendation and wish is that he stays but, ultimately, the board makes the final decision on those issues," Di Matteo told reporters of Cole. "That's ongoing. It's something he discusses directly with the club.
"Of course Ashley could get offers in January, but that is the world of football and that's how you live in this world, in this industry. Nobody knows what the future will hold. Ashley still has many years in front of him. He is a fit boy and can play in every game. He is definitely one of the best left backs in the world."
Should Cole decide to reject a one-year contract extension at Stamford Bridge, he could potentially reunite with a former Blues boss. PSG coach Carlo Ancelotti and Real Madrid boss Jose Mourinho are both said to be keen to link up again with their former charge.