The Red Devils were prepared to bid very high for Grealish if Paul Pogba left this summer.
But he looks set to commit his future to the club, and the form of Bruno Fernandes means a midfield target is less of a priority.
Grealish can also play on the wings, but may be the first backup option at several positions rather than a key starter for United if he joined.
Van de Beek would be significantly more affordable, and United have a good relationship with Ajax through past transfer negotiations.
After staying in the top-flight, Villa are expected to demand at least £80m for Grealish.