Manchester City are looking for midfield reinforcements following the injury to Kevin De Bruyne and have been looking at a few targets.
A move for Lucas Paqueta collapsed after the midfielder came under the scanner in a betting investigation and Nunes is now the top target.
Manchester City are pushing to sign the Portuguese midfielder with a little over a week left in the transfer window.
However, their opening bid for the Portugal international was rejected by the Midlands club.
Wolves knocked back an offer worth up to £47m from the Premier League champions for the midfielder.
The club paid a fee of £42m last summer to sign Nunes and do not want to sell him in the ongoing transfer window.
It could take a fee north of £60m to convince Wolves to part with their star midfielder this summer.
They are going through financial struggles and there are suggestions that at a certain figure, Wolves would not be able to resist selling Nunes.
