Ten Hag is close to finalising a deal to move to United, with sources telling ESPN that official confirmation of the Dutchman's appointment could come as early as the end of April.
Hamstra, who is the highest technical manager at Ajax after Marc Overmars resigned earlier this year, said that the club is now preparing both for him staying and leaving.
"We hope he stays. We have to stick with the facts, he has not left yet. He still is focusing on Ajax, so do we.
"We did everything possible [to keep him at Ajax]. We were very busy with that. He reacted that he is focussing on Ajax now. Now we are preparing for two scenarios, Ten Hag might stay or might leave."
The cup final was the third time Ajax and PSV met this season, with the two teams locked in a tight title race in the Dutch Eredivisie, and PSV denied the Amsterdam team their third successive Cup title under Ten Hag.
"Big clubs you dive into," Hiddink told ESPN NL. "It is important for Ten Hag to get the support and time he needs for all the work that needs to be done.
"That is important. I don't believe in 'risk of harm' as a coach. In a coaching career you fall once, twice, three times. Then you get back up your feet again."