Former Chelsea coach Portuguese Jose Mourinho is expected to be named as his replacement, reports Efe.
Van Gaal, 64, leaves after two years of a three-year contract with United.
The former coach of Holland spent two disappointing seasons at United, in which he only managed to lead them to win the Football Association Cup this season.
It is also still not certain whether assistant manager Ryan Giggs will stay on following the departure of van Gaal.
Giggs has been at the club for 29 years, winning the Premier League title 13 times, more than any other player.