The 21-year-old was in impressive form for his Dutch side during the 2021-22 campaign, scoring three goals and contributing two assists in 43 appearances in all competitions.
New Man United boss Erik ten Hag had allegedly identified the Netherlands international as a leading transfer target, but a potential move to Old Trafford has seemingly broken down.
Schreuder, who is Ten Hag's replacement in Amsterdam, is expecting Timber to stay with the club this summer, insisting that the defender "knows what is best for himself".
"I have spoken with Jurrien and I am assuming he is staying at Ajax. Timber is a smart guy and he knows what is best for himself. We think he is not done at Ajax yet," Schreuder told ESPN.
According to Dutch journalist Marcel van der Kraan, Timber had been closing in on a switch to Old Trafford before Netherlands manager Louis van Gaal warned him off a move to the 20-time English champions.
"Absolutely dead in the water. The player I think was ready to come, his agents went over to London, to Manchester United's officers two weeks ago, had very good talks. The money was never a problem," Van der Kraan recently told Sky Sports News.
"But then one man turned up, Louis van Gaal. He told the player in the Dutch camp, look if you go there I think your chances could be limited for playing for Holland in the World Cup three months later.
"Now for Jurrien Timber, a great Ajax style player, a ten Hag style player, that was a bit of a blow. Louis Van Gaal made it clear that he would not be in his Dutch team if he was playing every week for United."
The defender has made 74 appearances for the Amsterdam giants in all competitions, contributing four goals and two assists in the process.
"In the end, my gut feeling will be the deciding factor," De Telegraaf recently quoted Timber as saying when asked about his future. "The picture has to be right.
"You can go to a big club. But if you're not going to play there it's better to stay with Ajax. And Ajax is also a big club. We play football in the Champions League and I play there together with the best players in the Netherlands. That is not nothing.
"Of course, I can develop further [at Ajax]. I am 100% sure of that. I don't feel like I'm done at the club. But I can also develop at other clubs. I am now focusing on the upcoming international matches and then go on holiday. Then I'll have to think about it some more."
Man United have allegedly now switched their attention to Timber's Ajax teammate Lisandro Martinez, with the Argentina international currently being linked with a move to Old Trafford.
Antony is also said to be a leading target for the Red Devils, with the Brazil international starring under Ten Hag in Amsterdam during the 2021-22 campaign.