And Cole believes his former team-mate could be in for a new striker this summer with United rumoured to be interested in Paulo Dybala.
“Manchester United have always been a club that will buy centre-forwards, that’s the tradition of the club,” Cole told talkSPORT.
“I can’t see that changing, because they’ve already spent big money on centre-forwards.
“Will they add another one? Most probably they will, because to win the championship, to win anything you need to score goals and you need as many goals you can get in the team.
Man Utd boss Ole Gunnar Solskjaer to make transfer decision on striker for ONE reason (Image: GETTY)
Paulo Dybala has been linked with a move to Manchester United (Image: GETTY)
“So it wouldn’t surprise me if they bought another centre forward.”
The Norwegian recently stated that he is keen to bring fresh talent with the right attitude to Old Trafford.
He said: “We've tried to educate our players and our kids to be proper people. In my view, the best players have always been the best people.
"You have to have that value system and a certain kind of attitude about you to make a Man United player.
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Man Utd boss Ole Gunnar Solskjaer to make transfer decision on striker for ONE reason (Image: GETTY)
“You have got to have the qualities and our fans want to see exciting players.
"Of course we want to get up from our seats. We want to see defenders who defend like they're doing it for their lives - that's the most important thing.
"When we start games [against big clubs], our fans clap a striker making a tackle. It's always been in our culture.
"You have to have that work ethic and we're scouting the market, trying to find the right ones."