The Premier League champions have reportedly made Grealish their No.1 midfield target ahead of the summer transfer window, according to the Daily Mail.
Grealish, 25, has been the subject of intense transfer speculation with Man City's arch rivals Manchester United also keeping tabs on the star player.
But the Blues are hoping to pip the Red Devils to the signing of the England international by offering a monstrous deal that would smash the British transfer record.
Paul Pogba's £89 million transfer to Man United in 2016 is still the British record, with Man City breaking their club-record transfer with the signing of Ruben Dias (£64 million) last summer.
Pep Guardiola is a keen admirer of Grealish who has starred for Villa this season, scoring six goals and assisting 10 in the top flight.
But he faces competition from Ole Gunnar Solskjaer with Sir Alex Ferguson's former assistant Rene Meulensteen urging his old team to sign him.
He believes Man United should sell Pogba and use the funds they receive to draft in Grealish.
"I think with the stature of Pogba comes expectations. I don't think overall he's lived up to those for whatever reasons," said Meulensteen.
"So, if I could I would cash-in on him and reshape the team.
"The other problem is Pogba has never openly to the fans committed himself to Manchester United, how much he wants to play for this club. These are big issues for me.
"Declan Rice for me is a very young promising player, but playing for Man Utd is different playing week in week out. You need to be really coming up with the goods.
"I'm not too sure if he would be my pick there are other names touted around.
"A player like Grealish, he would have the DNA to play for Man Utd and the stature for it and he would have the ambition but it would change the outlook of the team. He is a ball hogger, he likes to dribble and create things for himself."
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