The Premier League champions have turned to the Portugal international after ending their interest in West Ham midfielder Lucas Paqueta, who faces an uncertain future as the FA investigate potential breaches of betting regulations.
City have reportedly had a £47m offer for Nunes rejected with Wolves apparently believing the 24-year-old is worth considerably more than that.
But City have a history of abandoning their attempts to sign players – from Harry Maguire to Declan Rice – when they felt the price exceeded their valuation and are willing to do so again if they cannot agree a suitable amount with Wolves.
However, Pep Guardiola described Nunes as “one of the best players in the world” after City faced Sporting Lisbon in the Champions League in 2022.
Wolves paid £38m for Nunes last summer but he has had an underwhelming spell at Molineux, scoring one goal in 40 games and being needlessly sent off in Saturday’s 4-1 defeat to Brighton.
However, the summer departures of the long-serving pair of Ruben Neves and Joao Moutinho meant he was shaping up as a key player for Wolves this season.
City’s search for midfield reinforcements was given added urgency when Kevin De Bruyne was ruled out for four months with a serious hamstring injury. They have signed Mateo Kovacic and defender Josko Gvardiol this summer while Rennes winger Jeremy Doku should become their third addition.