Blues boss Di Matteo has no fears the man he hailed as a Stamford Bridge "legend" would reach January in a position to be able to pen a pre-contract agreement with a rival club.
"I'm very optimistic that it will be dealt with before that," Di Matteo said after watching Cole net a vital late winner in the European champions' 1-0 victory over Stoke yesterday.
Di Matteo confirmed he had recommended to the Chelsea board that they keep Cole "as long as they can" before waxing lyrical about the 31-year-old, who controversially joined the club from Arsenal six years ago.
"He has become a legend - he is now Chelsea through and through," said Di Matteo.
"But I wouldn't say it's just happened recently. He's been here many years and has contributed a lot to this club."
Hailing Cole as an ideal example for Chelsea's new players to follow, he added: "He's a fantastic pro, which I'm not sure whether you know.
"Somebody that's the first one out in training, one of the first into the building with JT [John Terry], trains every day like a professional, reliable, somebody that you could go to war with.
"And he's a very quiet guy as well. He's very private at his own stuff.
"He's one of the best left-backs in the world."
It is said that Cole suffers from a persistent ankle problem that can limit his ability to train but Di Matteo said: "He's physically very good, very strong, has the ability to recover very quickly from game to game. Offers us a lot on that left hand side."
Cole does not offer many goals but asked whether he would urge Cole to get forward more often, Di Matteo said: "He'll have to buy me dinner. That's what I'm going to ask him.
"For two years, he hasn't scored and now he has, so he should buy me dinner."
Right-back Branislav Ivanovic, for whom goalscoring has never been a problem, said: "For me, Ash is the best left-back in the world - for a long time.
"He is really great, and always makes a lot of good things for the team.
"We're really happy for him because, for defenders, it is always nice to score goals for the confidence. Ashley is really fantastic.
"He has the skill, he has the speed, he can run, he can go up front, he has the vision of the game, he defends well, he is quick. But I think all this is nothing new!
"When he is ready, and his ankle is all right, he is the best.
"He can go on running a lot - I think more than other players."