It is believed Ajax have accepted an offer of £40m for the Netherlands international.
The 23-year-old must now agree personal terms and undergo a medical.
He will become Ole Gunnar Solskjaer's first signing of the summer.
The Red Devils have been scouting van de Beek for some time.
Their interest became more concrete when it was clear van de Beek would be keen on a move to Old Trafford.