Aston Villa were informed on Friday that City are willing to pay £90m for the 25-year-old, while highly rated winger Morgan Rogers has also been proposed as part of the deal. City value Rogers, 19, at around £10m, bringing the overall outlay close to Villa's £100m valuation of Grealish.
Aston Villa are keen to keep their captain, but sources have told ESPN that the decision will be left to the player.
City remain confident they can tempt the midfielder away from his boyhood club with the offer of Champions League football and the chance to consistently challenge for the Premier League title.
Sources have told ESPN that Rogers, who is also wanted by Crystal Palace after an impressive loan spell at Lincoln City last season, would be open to a move to Villa Park.
The teenager started the 2-0 preseason victory over Preston North End on Tuesday and had been earmarked by Pep Guardiola for a role in the Community Shield clash with Leicester at Wembley on Aug. 7. However, sources said Villa want a straight money deal.
City are keen to land both Grealish and Tottenham striker Harry Kane this summer.
Sources have told ESPN that City will not pay £150m for Kane but remain hopeful Tottenham chairman will be open to negotiations for the England captain. Kane, 28, has made it clear he believes it's the right time to leave Spurs in a bid to win trophies.
City have already seen Sergio Aguero leave the club this summer and will listen to offers for Bernardo Silva. Silva has been a key part of Guardiola's team that has won three titles in four years, but sources have told ESPN he is open to a move away from the Etihad Stadium.