Mourinho oversaw a disappointing sixth-place finish in his first season at Old Trafford but followed Louis van Gaal's FA Cup triumph with Europa League, League Cup and Community Shield glory.
The 1999 Treble victor told ESPN FC: "I look at him at the moment, he's scoring goals and he's bringing a lot more things to his game".
The England worldwide also described the difficulty of consecutively winning trophies year after year and how he wants help make Old Trafford a fortress.
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"I think he will end up as a centre-forward", he added. I just think at the moment having Lukaku in the team and obviously Zlatan [Ibrahimovic] coming back as well, I think it's good.
"I'm hoping he [Martial] is going to be there a long time", said a man who netted 121 times for the Red Devils. Cole thinks so, but things are good at the moment, so no need to rock the boat with Martial's development and make him complacent, that's something Mourinho always tries to avoid.
"It's definitely coming back, but where they were to where we are now, we've still got a long way to go because they were consecutively winning", he added.
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Eden Hazard opened scoring for Chelsea in the 21st minute of the game through a penalty. And the trio combined to double the lead in fine style eight minutes before half-time.
But if you want to see a keeper play out the back like never before, just wait until Marcus Rashford gets himself between the sticks.
On Saturday, Rashford started alongside Anthony Martial, marking only the 12th time the duo have been on the pitch at the same time in their careers.
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"If you look at the talent that kid's got, it's absolutely frightening".
"I look at him at the moment, he's scoring goals and he's bringing a lot more things to his game", Cole told ESPN FC.
They loved it and United's attack certainly looked threatening with the trident of Rashford, Martial and Romelu Lukaku.
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However, while the Old Trafford faithful were both elated and impressed with his display, they also spotted an extraordinary play from Marcus Rashford, in the build up to his cushioned-header assist to Pogba.