The American keeper played at Old Trafford from 2003 until 2006, around the time Rashford graduated from Fletcher Moss Rangers to United's academy as an eight-year-old.
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".
Asked how good the 20-year-old England forward can become, he added: "That's up to him".
The main talking point of Manchester United's emphatic 4-1 win over Newcastle on Saturday, was the return of Paul Pogba, as the Frenchman put on a dazzling display, both scoring and assisting on the day - emphasising what the side had been missing for the last two months in his absence. I think we're on a path back to doing that. "But teams are coming to have a go and we want to get rid of that".
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.
Against Newcastle, Rashford started on the right with Martial on the left, either side of Lukaku, but it was not until Rashford moved inside, with Juan Mata taking up his position on the right, that United began to look unsafe.
"I'm hoping he [Martial] is going to be there a long time", Cole said.
Rashford's form and standing in the eyes of Mourinho is now forcing Anthony Martial to be patient in his pursuit of regular minutes, with the Frenchman having made more of an impact off the bench this season than from the start.
"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", he told ESPN.
Manchester United manager Jose Mourinho admits it is a delicate act balancing the game time of Marcus Rashford and Anthony Martial.
Ibrahimovic's return to first team action has raised questions over which strike pairing Mourinho might use in the coming weeks.
"So to play them [Martial and Rashford] together gives us things but also takes some things from us".
"You've got Rashford, you've got Martial - they're all quality players and they all know what to do".