The Portuguese manager has been heavily tipped to move back to Stamford Bridge following his revelation that he wants to be at a club where he is "loved".
"He's a great guy, I owe him a lot and we had some great successes together," Cole told talkSPORT. "Chelsea fans and the media would love to see him back, he's great value.
"He's the best manager in the world at the moment. I'd love to see him back - for the [good of the] Premier League as much as anything. Imagine him going up against Sir Alex Ferguson again. I hope he comes back."
Mourinho left Chelsea in 2007 following a reported fall-out with club owner Roman Abramovich.