The Red Devils are reportedly willing to part with £35m to make the deal happen and could even wrap up a deal by the end of next week.
The 27-year-old had earlier dismissed reports that he was headed for Old Trafford by claiming that he had no intention of moving to England.
After signing Ander Herrera and Luke Shaw and having interest in Angel di Maria, it would seem likely that United’s spending could break the £100m mark in the coming weeks.
Di Maria is set to leave Spain following the arrivals of James Rodriguez and Toni Kroos at the Santiago Bernabeu, and could set the Premier League club back by around £45m.
Vidal has been linked with a switch to English football for months, with Liverpool also interested in adding him to their Champions League squad, but United has always appeared to be the most likely destination.
Van Gaal’s side are currently on a pre-season tour of the United States and, after their 7-0 demolition of LA Galaxy, laboured to a 3-2 victory over Roma this weekend.