The Manchester Evening News says United have ramped up their interest in Grealish and are 'keen on agreeing terms this month' to stop his fee rising after Euro 2020.
The Red Devils hope to bag the 24-year-old playmaker early in the summer transfer window, but want to 'execute' a deal in February.
Grealish is expected to make his England debut this year and could be a part of Gareth Southgate's Euro squad.
The Premier League giants will need to trigger the Villa captain's release clause - reportedly £45million - to get him before his contract ends in 2023.
Grealish is understood to often party in Manchester as a change from his home city of Birmingham.