The 24-year-old, who has scored nine times and contributed seven assists in 27 appearances for Villa this season, is believed to be on the radar of a number of clubs ahead of this summer's transfer window.
Barcelona, Real Madrid and Manchester City are all thought to be interested in the Englishman, who is thought to be valued in the region of £60m by Dean Smith's side.
However, United would allegedly be Grealish's number one choice if the attacking midfielder left Villa Park in search of pastures new at the end of the 2019-20 campaign.
According to Goal.com, formal transfer talks between the Red Devils and Villa are yet to take place, but the player has approved a move to Old Trafford this summer.
The report claims that Grealish has already started house-hunting in Manchester ahead of a potential switch to Ole Gunnar Solskjaer's side.
The attacker, who is being tipped to earn a spot in the England squad for this summer's European Championships, is Villa's leading scorer in the Premier League this season with seven goals. body check tags ::