Di Matteo was opposed to a blanket ban on offering players over 30 anything longer than a one-year deal, saying: "You would have to look at it individually, every player, depending on the history and the physical condition of every player."
And he had no doubt Cole fit the bill, hailing the defender as "absolutely", "certainly" and "no doubt" one of the best left-backs around.
He added: "He's a fit boy. He can play every game, so he still has many years in front of him."
The former Chelsea midfielder refused to say how he would have responded to a one-year contract offer when he was a player.
"That's something you would have to ask Ashley himself or the club," he said.
"These negotiations between those two parties. My point is that I would like him to stay here and be here with us."