The club and 62-year-old Van Gaal, currently coach of Holland, are understood to have reached a broad agreement but no deal has yet been signed.
United are due to announce their third-quarterly financial results later on Thursday but this will not include any announcement about the permanent successor to David Moyes.
Van Gaal is busy with preparations for Holland's friendly against Ecuador at the Amsterdam ArenA on Saturday, and sources close to the club have ruled out any announcement taking place either side of that fixture.
United's interim manager Ryan Giggs was photographed leaving a hotel in the Dutch town of Noordwijk on Wednesday, where it is understood the 40-year-old had a meeting with Van Gaal.
Giggs' playing contract expires in June and he is expected to be offered a senior coaching role, though it is not known whether he intends to keep playing next season.