Aston Villa are tipped to accept a £100m offer from Manchester City for Grealish, with the final decision over whether the move goes through being left to the attacking midfielder.
Grealish will make up his mind in the coming days whether to link up with Pep Guardiola once he returns from holiday in Croatia.
If the midfielder does go then Aston Villa will launch a bid to take Cantwell from Carrow Road.
They have already done business with Norwich this summer, completing the £38m signing of Emiliano Buendia.
However, Norwich are in no mood to send another player to Villa Park and have no intention of selling, with only a huge offer likely to change their stance.
Norwich are trying to sign PAOK Salonika winger Christos Tzolis, but he is not seen as a replacement for Cantwell.
Aston Villa are meanwhile set to make another signing after agreeing a fee with Bayer Leverkusen for winger Leon Bailey.