Ten Hag has been repeatedly linked with the permanent United job, which will become available at the end of the season when Ralf Rangnick moves into a consultancy role.
The Dutchman and Mauricio Pochettino appeared among the favourites for the Old Trafford role, though reports in the last week suggested Ten Hag has all but agreed on a deal.
Hamstra, who is the highest technical director at the Eredivisie champions after Marc Overmars departed earlier in the year, insists Ajax have left no stone unturned in their attempts to retain Ten Hag.
"We have done everything we can and are doing everything we can to keep him on board," Hamstra told ESPN.
"Contract extension offered? Yes. More money? Everything that comes with it, without going into detail."
Hamstra was speaking before Ajax's 2-1 defeat to PSV in the Dutch Cup final, the latter side scoring twice in as many minutes through Erick Gutierrez and Cody Gakpo to secure victory.
The two teams are also locked in a battle for the Eredivisie title, with Ajax four points clear ahead of the final five games.
If the reigning Eredivisie champions can retain their crown, it would be their third league title under Ten Hag, who guided them to the 2018-19 Champions League semi-finals before a last-gasp loss to Tottenham.
While Hamstra is keen to see more from the 52-year-old, he conceded the decision remains in Ten Hag's hands.
"Erik can ultimately determine his own future. He is old enough and wise enough for that," he added.
"We have two scenarios: we really hope he stays; it makes sense that there is interest in him. If he doesn't stay, we have to be ready for the second scenario."