City had ramped up their interest in Nunes this week as they look to bolster their midfield options.
A serious injury to Kevin de Bruyne that will see the Belgian miss four months of action has hastened plans to bring in a replacement.
Nunes has been monitored throughout the summer but City have now seen a bid of £47m rejected by the Molineux outfit.
Wolves are under no pressure to sell and believe the offer is well below their valuation of the Portugal international, talkSPORT understands.
The Premier League side do not want to lose Nunes so late in the transfer window and without a replacement in sight.
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The former Sporting star has been a key performer for Wolves since signing in 2022 and has been linked with Liverpool throughout the year, as well.
Wolves forked out a club-record fee for Nunes at the time, signing him for £38m.
A bid of £47m would hardly represent the best of deals for Gary O'Neil's side considering the fee they had already brought him in for.
They have also lost plenty of players already this summer, including Ruben Neves, Raul Jimenez, Conor Coady and Nathan Collins.
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Pep Guardiola is a long-term admirer of Nunes after City played Sporting in the Champions League in 2021.
"Sporting is a fantastic team," Guardiola admitted his his post-match press conference after the match.
"They are the champions of Portugal, which has a very strong league, with FC Porto and Benfica, they change the ball well, they have fast and intelligent players.
"Matheus Nunes is one of the best players in the world today.
"Despite the difficulties and some mistakes, I have to be very satisfied because we took a big step towards the next round. Nunes is one of the best at the moment."
City are closing in on the signing of Jeremy Doku from Rennes in a deal worth around £55m.
The Belgium international is set to replace Riyad Mahrez on the right-wing after the 32-year-old signed for Al Ahli earlier in the transfer window.