Ten Hag, 52, has been in charge at Dutch giants Ajax since December 2017 but he has been repeatedly linked with the United hot seat this summer, with Ralf Rangnick set to move into a consultancy role.
Paris St Germain head coach Mauricio Pochettino was also on United’s wishlist but the Athletic has reported Ten Hag has verbally agreed to take over from interim boss Rangnick at the end of the season.
The PA news agency has contacted United for comment.
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Rangnick agreed to take interim charge of United last November following the sacking of Ole Gunnar Solskjaer.
The club face missing out on the Champions League next season as they sit three spots and six points adrift of fourth-placed Tottenham in the Premier League with seven games of the campaign remaining.
But that seems to have been no obstacle in attracting another standout European coach, with Ten Hag winning the Eredivisie and Dutch Cup twice while he led Ajax to the 2019 Champions League semi-finals.
Ajax are on course for another domestic double – they are four points clear of second-placed PSV Eindhoven and will take on their rivals in the final of the Dutch Cup this weekend.