Ait-Nouri, who has scored 12 goals in 157 appearances for Wolves, is on the verge of joining the eight-time Premier League champions after a four-and-a-half year stint at Molineux.
The Algerian international initially arrived on loan from French club Angers in October 2020, before completing a permanent move for £9.8 million the following summer.
Wolves have taken out the 50 per cent buyout clause from Angers before the City deal goes through.
Ait-Nouri registered his highest goal scoring season last term - netting five times and setting up seven more in 41 matches across all competitions.
His imminent departure comes just days after Brazilian international Matheus Cunha completed his £62.5 million switch from Wolves to Manchester United.