Rashford has established himself as one of United’s first choice strikers this season, alongside Anthony Martial.
With Martial injured, Rashford has had an extended run down the middle but has failed to make the position his own and will now miss a run of games with a groin injury.
Cole had previously stated that Ole Gunnar Solskjaer should build the Man Utd team around Rashford but the ex-United man believes Rashford needs to learn from two of the Premier League’s best strikers to improve his game.
Cole told BBC Radio 5Live: “I want to see from Marcus, I know the two are totally different players but if you’re going to play that position, I want to see Aguero. I want to see Firmino.
“That’s what I want to see. If you look at those two guys playing as a number nine, when I watch them, I get excited watching them.
“Aguero for me, and I keep saying it, is the best centre-forward in the Premier League. I love this movement, I love that he just wants to get in the box, I want to score goals, I don’t care what it is, header, tap-in, I’m going to do it and I know what I’m going to do.
“Firmino for Liverpool, he brings people into the game, he sets people up but I’m still going to get in and get my fair share as well.
“I look at those two and I say to myself I just love watching you two play centre-forward.
“Marcus has got to learn off those kinds of individuals.”
Cole picked out Mason Greenwood for praise, believing he has the ability to be top class but urged patience from the club and the fans.
The Englishman is likely to start up front on Monday night against Arsenal, with Rashford and Martial expected to be out of action.
Cole added: “He has got a chance. His finishing is a joke, left or right foot, he’s got quality in abundance.
“I just hope they don’t, Manchester United won’t anyway, put too much undue pressure on him. He’s got great ability.
“The disappointing thing is, he’s going to have to get thrown into the deep end a little bit earlier than they would have liked due to injuries, due to being prepared to let Lukaku and Sanchez go.
“They’re looking at it and thinking we’ve got Mason, we’re going to give Marcus the opportunity to play centre-forward.
“Ideally, it would have been nice if they’d bought themselves another centre-forward.”