The pair have worked together before, with 29-year-old Vlaar having featured prominently in Van Gaal's Netherlands side that reached the semi-finals of the World Cup in Brazil during the summer.
It has been widely speculated that Van Gaal is eager to bolster his defensive options at Old Trafford this winter, with Borussia Dortmund's Mats Hummels thought to be near the top of his shortlist.
However, Van Gaal has accepted that the German international is unlikely to be allowed to leave Dortmund halfway through a season, which has brought about his interest in Vlaar, according to the Sunday Express.
Vlaar's contract with Villa is due to expire at the end of the season and he is thought to be in no rush to commit to fresh terms.
The report added that Vlaar, who would be keen to join Van Gaal at United, could command a fee in the region of £4m.