The Dutchman 52, is one of the names being touted to take over the reins at Old Trafford and replace interim-manager Ralf Rangnick.
Sources have claimed United chiefs met with Ten Hag last month to interview him about the role.
They would have to pay £1.7million to Ajax in order to release him from his current contract.
But ex-Everton midfielder Klaassen is keen to see Ten Hag rebuff United's advances and stay in Amsterdam.
"He has been doing well with us for years and Manchester United has been doing badly for years," the former Everton player told Voetball Primeur.
In response to suggestions Ten Hag could go, Klaassen added: "He can also stay. I hope so."
Klaassen's comments follow some from Ajax forward Sebastien Haller who remains optimistic he will stay in the Netherlands.
The ex-West Ham striker, who previously worked under Ten Hag at Utrecht, warned United last week over trying to tap up the his boss, but said he would not look to influence any decision.
Haller, 27, also suggested he would be intrigued to see how his current manager might fare if he took the Old Trafford job, but says he may have to adjust his approach in England.
He said: "Every dressing room is different and every team is different. Then you have to act differently, depending on the selection you have at your disposal. We'll see how he will do.
"I know how good Ten Hag is tactically. He always has a good view of the opponents. With that he gives us the key to win a match.
"We all understand if he did it, but I think it's up to the coach to choose what he wants. We're just his players.
"I'm just grateful for what he has done for me and I hope he will make the best decision for himself."
Ajax won their game at the weekend beating FC Groningen 3-1 away, while second placed PSV Eindhoven dropped points, drawing 3-3 with FC Twente.
The gap at the top of the Eredivisie is now five points, as Ten Hag closes in on a third domestic title.