United are allegedly determined to sign the Englishman ahead of the 2020-21 campaign despite suggestions that Villa value their captain in the region of £80m.
The 24-year-old has been in impressive form for Dean Smith's side during the current season, scoring nine times and contributing eight assists in 32 appearances in all competitions.
According to The Athletic, Grealish is currently fully focused on helping to keep his team in the Premier League, but the attacker will seek pastures new during this summer's transfer window.
The report claims that United are 'leading the chase', although it remains to be seen whether Ole Gunnar Solskjaer's side are prepared to meet Villa's seemingly seemingly substantial asking price.
Grealish's existing deal at Villa Park is due to run until the summer of 2024.