Van Gaal, the former Ajax, Barcelona, Bayern Munich and current Holland coach, is widely expected to be confirmed as United's new manager in the coming days.
If appointed, the Dutchman would inherit a squad that has slipped to a low ebb after finishing seventh in the Barclays Premier League and failing to qualify for the Champions League.
Cole feels the vastly experienced Van Gaal, 62, has the gravitas to steer the club back towards the top after a season of frustration under David Moyes, who was sacked in April.
Cole, speaking at bwin's 'Play at Old Trafford' event, said: "We are hoping this is the one that can bring us success again.
"It has only been one season when we haven't won anything - that is how crazy it is, that it is doldrums - but he has got the experience of managing at big football clubs.
"He has not managed in England but experience is massive, especially at a football club of this magnitude.
"He has European experience, knows how to deal with big-name players and has a history of bringing through kids as well.
"To have managed at those clubs he has managed at, you need something special.
"To see us playing the way we played last season was very difficult. It was upsetting and we had to take a bit of flak as well.
"But that is football. We have to bounce back from that and say, 'Next season is a new season, let's get the show back on the road'."
The obvious void for United next season will be the lack of European football.
Next season will be United's first outside the Champions League, a competition they won in 1999 and 2008, since 1995-96.
Cole fears that could have a negative impact when it comes to signing players this summer.
Cole, a member of United's treble-winning 1999 side, said: "To try to entice players to come to Manchester United without the European Cup, they are going to have to do some salemanship.
"That could be tough. The European Cup is a massive competition and all the top players want to play in it.
"Fingers crossed we will be able to get the players we need to make us compete next season for the Premier League and to get back into Europe.
"This is one of the biggest football clubs in the world. To not have European football next year - I don't know what I am going to do with my Wednesdays! No Man Utd in the European Cup? It doesn't sound right."
Cole's former team-mate Peter Schmeichel does not think the current squad needs a major overhaul, but also believes the hand of an experienced manager is essential.
Schmeichel, United's goalkeeper from 1991-99, said: "It looks like it is going to be Van Gaal and it is going to be announced some time soon.
"If it is him it is a very strong experienced manager. I think it is probably what the club wants now - someone with a direction, someone who can take charge and someone who has experience enough to withstand whatever pressures he would be facing.
"It is not major surgery that is needed, just little tweaks that if you combine can have an enormous effect. I don't think we are a million miles away.
"But I still think we need to sign players for a variety of reasons.
"First of all we need players, then we also need new inspiration and then we need, as a football club, to make statements.
"We need to say, 'Yes we had a bad season but we have got the powers to attract the top players'.
"I think those kind of statements are very important, to supporters, the outside world and to the squad.
"That would go a long way to restoring some of the confidence the squad lost in the season just gone."