He can see major improvements in the squad since Solskjaer took charge of the club and saw the opening day defeat to Crystal Palace as a minor set-back.
Speaking on the Football Times podcast, Cole said: “I genuinely do believe he needs to be given time.
“When you look at when he took over, where the team, where the squad was at then to last season finishing fourth and getting to three semi-finals, that is improvement.
“I do believe they'll finish in the top four. They've got 37 games to turn it around, that's a long, long time.
“Me and Ollie were always cool. We had a good relationship, we always used to have a laugh and joke, always used to work on our finishing together.
“I’ve had the opportunity to speak to him quite a few times since he's had the job as well and he doesn't talk to me like I'm no longer his teammate. We talk like we're still teammates. That speaks volumes about Ollie.”
However, while Cole is optimistic about the season ahead, he still wants to see new signings arrive at Old Trafford, though ongoing lockdown uncertainty could scupper plans to make big money moves.
“Of course every team needs a few more signings, but financially, if you're talking about the signings they're talking about, it's big money.
“If you've got no revenue coming in but money going out, it's not easy. They've got to find the money from somewhere.”
United face Brighton this weekend in a bid to shake off disappointment from their 3-1 defeat to Crystal Palace, and Cole is backing them to do just that.
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“You go through things like that in a football match. Take nothing away from Crystal Palace but Manchester United weren't up to speed, Palace were, and they deservedly won the game.
“You move on, you start again this weekend against Brighton and you go from there.
“Anything is possible when it comes to Man Utd, I'm looking for a more well-rounded performance, even if it's away. Brighton will be a very tough game.”
The BT Sport Monthly Pass lets you watch BT Sport for a simple monthly fee of £25 with no contract. Customers can watch all BT Sport Premier League fixtures for the next 30 days including Brighton vs Manchester United from 11:30am on Saturday 26th September. For more info visit bt.com/monthlypass.
For the full breakdown of what games are coming up check out our Premier League fixtures on TV guide.
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