The 41-year-old believes the England striker would represent too big a loss for David Moyes' side and expects him to remain at the club, while also praising the former Everton boss
Cole, however, believes the 27-year-old will stay with David Moyes' side as he would represent too big a loss for the club were he to leave.
"Everyone wants him to stay. He's a wonderful player. If you lose a quality player like that you're going to be disappointed," Cole said in Australia on Monday.
"I do believe he's going to stay at Manchester United which is the most important thing."
Cole is also confident that new boss Moyes will succeed at United, despite being under immense pressure to deliver results in the wake of Sir Alex Ferguson's trophy-laden 26-year stint at the club.
"David Moyes has come in. He's done a wonderful job at Everton and I wish him well at Manchester United," he continued.
"I think we all know it's going to be a very, very tough job to follow Sir Alex Ferguson but I really do believe he'll do a very good job.
"Manchester United gave David Moyes a six-year contract so they believe in him. Naturally they're going to give him time.
"Football now is always guided by results. It's a results-driven business. As Manchester United, we're very spoilt and very privileged that we've won so much over the past 25 years.
"We want it to continue, naturally, but everyone wants to win the big prizes. We know we're going to find it tough but I think David Moyes will do a very good job."