The 18-year-old impressed during a loan spell at Notts County last season before making his Villa debut against Manchester City in May.
The highly-rated youngster has one year remaining on his current deal at Villa Park.
According to the Daily Star, Villa have offered Grealish fresh terms but he is stalling on signing a new deal, which has alerted Chelsea.
The West London outfit, who are said to be keen to do business quickly, could swoop for the Republic of Ireland Under-21 international as soon as January.
Grealish has made three appearances for Villa this season.