Wolves midfielder Nunes. AFP
It is understood the Premier League champions have agreed to pay Wolves £47 million ($60 million) without add-ons but the deal has not yet been finalised.
In a separate deal, City's 21-year-old midfielder Tommy Doyle will join Wolves on loan with an option to buy.
City had a previous bid for Nunes rejected, with the 25-year-old subsequently choosing not to train with Wolves in a bid to force through a move in the final days of the transfer window.
Speaking after Tuesday's 5-0 League Cup win over Blackpool, Wolves boss Gary O'Neil said he was unaware of any improved bid from City and expected the player to remain at the club beyond Friday's deadline, but that situation has quickly changed.
Nunes became the Premier League club's then record signing when he joined from Sporting Lisbon for an initial £38 million last year.
He made 34 top-flight appearances last season, scoring one goal.