The Dutch daily said first talks between the parties began a fortnight ago, before the sacking of David Moyes, and that an agreement was reached on Friday night after talks with one of the Glazer brothers, club director Ed Woodward, and a club lawyer at Van Gaal's holiday home in Portugal.
The America-based Glazer family own Manchester United and would give Van Gaal a budget of 100 million Euros to spend on new players, it said on its website.
Dutch broadcaster NOS quoted national team media officer Kees Jansma as saying on its website: "He told me that nothing definite has happened but there has been discussions. He expects to be able to say something not later than next week."
Van Gaal has been the bookies' runaway favourite to take over after the sacking of Moyes this week.
Former manager Alex Ferguson has, however, backed, interim manager Ryan Giggs, whose first match in charge is against Norwich City on Saturday, as the club's full-time boss, British media reported.