Having contributed eight goals and six assists on the way to helping Villa remain in the Premier League, Grealish is being heavily linked with a switch to Manchester United.
According to Sky Sports News, Arsenal have also made enquiries with regards to the availability of the Englishman.
However, the report adds that the Gunners were quickly put off by Villa's valuation, said to be in the region of £80m.
That stance allegedly leaves it increasingly likely that the 24-year-old will spend at least another season in the West Midlands.
Grealish still has three years remaining on his contract.