Ten Hag was announced as the Premier League club's new head coach last month, but he will not officially take charge of the 20-time English champions until the end of the campaign.
The 52-year-old has already led Ajax to this season's Eredivisie title, though, and the Dutch outfit's final match of their 2021-22 campaign is against Vitesse on Sunday afternoon.
Ten Hag has been in charge of Ajax since December 2017 and will step down having delivered three Eredivisie titles and two Dutch Cups.
Ralf Rangnick will lead Man United out for the final time against Palace, with the German stepping aside to become a consultant for the club, in addition to managing Austria.
According to The Athletic, Ten Hag wants to be in the stands for the match with the Eagles, as he begins his plans for the 2022-23 campaign.
However, it is alleged that a decision has not yet been made whether the Dutchman will be at Selhurst Park or watch the match from another location.
Man United will not be in the Champions League next season due to their struggles, with the club instead battling West Ham United for a position in next year's Europa League, sitting sixth in the table, three points ahead of the seventh-placed Hammers, who have a game in hand.
The 20-time English champions will post their worst ever points total in a Premier League campaign regardless of whether they manage to pick up all three points away to Palace next weekend.
Ten Hag is expected to have around £100m to spend on new players this summer, although the figure could rise depending on whether there are any big-money outgoings.
The club's wage bill will also be trimmed significantly with the departures of Paul Pogba, Nemanja Matic, Juan Mata, Edinson Cavani and Jesse Lingard on free transfers.
Ten Hag is allegedly determined to sign Barcelona midfielder Frenkie de Jong this summer, having had the Netherlands international at Ajax.
Meanwhile, another of his former players, Matthijs de Ligt, is believed to be a target, with the Juventus centre-back potentially available for transfer during this summer's transfer window.
Man United also believed to be keen to add another forward to their squad, with Benfica's Darwin Nunez viewed as their leading target, having been priced out of a move for Tottenham Hotspur's Harry Kane.
Cavani is certain to leave at the end of his contract, while there is uncertainty surrounding the futures of Anthony Martial and Marcus Rashford.
Cristiano Ronaldo, though, has seemingly confirmed that he will be a part of the squad next term, with the Portugal international hailing Ten Hag's work at Ajax.