The Englishman has been linked with a switch to Old Trafford for some time and is widely expected to depart Villa should they suffer relegation come the end of the season.
Clubs are likely to be severely financially-restricted during the summer transfer window in the wake of the coronavirus pandemic, but United are supposedly determined to get a deal for Grealish over the line ahead of the 2020-21 campaign.
According to The Express, Ole Gunnar Solskjaer's side are confident of securing Grealish's signature and have identified the Villa captain as an ideal replacement for Angel Gomes, whose contract at Old Trafford is about to expire.
The report claims that Grealish is already making preparations for life in Manchester and has found a house to buy, but Villa will hold out for a fee of £80m even if they make an immediate return to the Championship.
Grealish has registered nine goals and eight assists for Dean Smith's side in all competitions this term and has three years left to run on his current deal at Villa Park.