The attacker is one of the many who the Red Devils are assessing ahead of a busy transfer window.
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Per Florian Plettenburg, the Dutchman is said to have met Erik ten Hag about making the switch.
Zirkzee will also get a chance to work with another Dutchman at United in Ruud van Nistelrooy, who will be first team coach.
The Red Devils are hoping to seal a move for the forward by paying his release clause.
However, they still have to agree terms with both the player and his agent Kia Joorabchian.