Grealish, 29, was on the fringes of City's squad last season, with his prospects further diminished by the recent signing of French midfielder Rayan Cherki.
The winger, who joined City from Aston Villa for a record £100m, was previously left out of the Club World Cup squad by mutual agreement.
This potential move aligns with Everton's efforts to strengthen their squad after finishing 13th last season and moving into their new Hill Dickinson Stadium.
Everton have already been active in the transfer market, recently completing the £25m signing of Kiernan Dewsbury-Hall from Chelsea, their fifth major acquisition this off-season.