The Premier League champions have been repeatedly linked with the England international this summer.
The Premier League champions have been repeatedly linked with the England international this summer and it is now claimed that they have made an official approach for the 25-year-old.
City declined to comment when contacted and Villa have also remained silent on the issue.
Grealish, who has four years remaining on his contract at Villa Park, would command a high fee.
Villa are reportedly reluctant to sell and are prepared to offer the player fresh terms but a significant offer could test their resolve.
Grealish has emerged as one of the hottest properties in the English game due to his talismanic performances for Villa. He scored six goals in the Premier League last season and also provided 10 assists. He then made four appearances for England during their run to the final of Euro 2020.
He is one of two players at the centre of considerable transfer speculation involving City this summer, with the other being Tottenham and England captain Harry Kane.