The 49-year-old has been linked with a number of high-profile jobs since leading Ajax to the UEFA Champions League semi-finals and a domestic double last season.
Among Ten Hag's rumoured suitors is German champion Bayern Munich, which has placed Hansi Flick in interim charge until the end of the campaign.
Bayern has been tipped to make an approach for the Dutchman ahead of next season, but Overmars is adamant his compatriot is going nowhere.
"Ten Hag can easily last another season after next summer," he told De Telegraaf.
"I certainly won't let him go yet, although I know that he is on lists at major European clubs. That door will remain closed for the time being."
Ajax could also face a fight keeping hold of attacking midfielder Hakim Ziyech, who has nine goals and 16 assists in the UEFA Champions League and Eredivisie this term.
Overmars is hopeful the Morocco international will stay put in Amsterdam and become a club legend, but is realistic about Ajax's chances of keeping him.
"With Hakim, I regularly think he has reached his ceiling but every season he takes another step," Overmars said. "I sometimes tell him he can become Mr. Ajax, so why leave?
"But if we're being honest, he is 27 years old and at his peak. If he can make the step he has in mind then of course it would be allowed of us."
Donny van de Beek is another player in demand and is soon to enter the final two years of his existing contract.
"Next summer I expect a lot more interest in our players," Overmars said. "It becomes harder to keep our squad intact. Ajax players are loved everywhere.
"Think of Van de Beek and Ziyech. They have been here a long time and have brought Ajax so much beauty."