The 23-year-old left-back has emerged as a major target for Pep Guardiola’s team, who are increasingly confident of completing a deal despite no discussions having yet taken place between the clubs.
Things are expected to accelerate in the coming days, with City keen to get the deal done before they fly out to the Club World Cup on June 12.
Wolves’ current valuation of Ait-Nouri is not known, though they have previously rated the Algerian at around £50million and will demand a high price for a player who has made more than 150 appearances since first joining on loan five years ago.
Angers still hold a 50 per cent sell-on clause which was part of the £10m permanent deal which brought Ait-Nouri to Molineux in 2021.
Wolves have the option to buy-out the clause for £9m and will trigger it before any move to City is completed.
Ait-Nouri scored five goals in 41 appearances in all competitions last season, cementing his place as a key member of the starting XI.
With one year remaining on his existing deal and the option for a further year, Wolves were prepared to offer him a new contract but no formal discussions ever took place and the interest from City is now likely to make them redundant.
City, who failed to win the Premier League for the first time in five seasons, are aiming to recruit players with top-flight experience this summer.
Wolves now look to be facing a significant shake-up of their squad with Ait-Nouri likely to follow Matheus Cunha out of the door.
The latter has joined Manchester United after they triggered a £62.5m release clause in his contract, signed last January.
Another forward, Pablo Sarabia, is leaving after the expiry of his contract while doubt surrounds the future of captain Nelson Semedo.
The Portugal international, who is also out of contract, has been offered a new four-year deal but is still to decide whether to sign it.
A farewell video to supporters, should he choose to depart, has already been recorded.