The England international is understood to have been the subject of a £100m bid from City last week, although Villa remain determined to keep him on the books.
According to the Daily Star, City chairman Khaldoon Al-Mubarak remains confident about his side's chances of completing a nine-figure deal for Grealish and is anticipating the 25-year-old telling Villa that he is keen on a move this week.
Grealish has been enjoying an extended break since his Euro 2020 exploits with England, and he boasts a total of 32 goals and 43 assists from 213 games in Villa colours.
However, should City's pursuit of Grealish end up proving successful, the Premier League champions will reportedly end their interest in Tottenham Hotspur's Harry Kane for the time being. body check tags ::