The Manchester Evening News says United have expressed interest in signing Grealish, 24, early in the summer transfer window after they finalised their shortlist of playmaker options last month.
United's preference is to 'execute' deals for summer targets in February.
United are conscious Grealish could make his England debut before the end of the season and then feature at the European Championship, causing his valuation to soar. Villa have not confirmed whether Grealish, contracted to the club until 2023, has a reputed £45million release clause.
Grealish often socialises in Manchester to escape the Birmingham bubble and United are believed to have previously enquired about the Villa talisman.
January signing Bruno Fernandes has had an influential impact, scoring one and assisting two in the wins over Chelsea and Watford last week, but his arrival has not impacted United's interest in attacking midfielders Grealish.