The Villans lost 1-0 at Wembley on Saturday, with Cottagers midfielder Tom Cairney hitting the game's only goal in the first half. The result means Steve Bruce's side will have to play Championship football once again in 2018/19.
The Sun claim United are considering a move for Grealish, who is a wanted man after an impressive season at Villa Park.
Grealish displayed quality that would not look out of place in the Premier League, and he will have been massively disappointed not to get back to the English top flight - but the transfer market could see him still get there.
The Red Devils are looking to prepare for the long term this summer and 22-year-old Grealish shouldn't break the bank.
Club scouts are said to be impressed by the star's ability to drive forward from deeper positions in midfield - currently, Paul Pogba aside, Jose Mourinho has no such player.
Meanwhile United continue to be linked with Shakhtar Donetsk star Fred, with reports last week suggesting a deal is in place.
Mourinho and Ed Woodward are expected to be a busy men this summer, as they seek to rebuild in a bid to close the gap between themselves and neighbours Manchester City.