Sky Sports says City made initial contact with Villa a few days again and negotiations are still open.
Villa have extended a new contract to Grealish in the hope he'll stay with his boyhood club.
Any deal depends on whether City are willing to meet Villa's valuation, currently at £100m.
Grealish has been linked with City all summer but now things have started to get serious.
It is expected City will have to sell a few players before coming close to Villa's asking price.
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