City have reportedly reached a verbal agreement with Wolves for the Portugal midfielder with youngster Tommy Doyle heading in the opposite direction separately, as per transfer guru Fabrizio Romano.
According to The Athletic, the deal is thought to be worth around £47 million while the move for Doyle will be a loan with an option to buy at £5 million plus a 'significant' sell-on clause.
City had an initial offer for Nunes turned down earlier in the window which then prompted the 25-year-old to fail to report for training in order to push for a move.
On Tuesday, Wolves manager Gary O'Neil said he "expected" Nunes to remain with the club for the time being but had soon been anticipating a resolution to his future.
Wolves signed Nunes from Sporting last summer on a five-year deal and has made 41 appearances for the club.
Doyle, meanwhile, spent last season on loan at Sheffield United, playing a role in the Blades' promotion to the Premier League.