Matheus Nunes has made two appearances for Wolves this season
The deal for the 25-year-old has not been formally agreed yet but if completed, there will be no add-ons.
City had a previous bid for the Portugal international rejected last week, with Wolves believed to be wanting in excess of £60m.
Nunes has been absent from training recently after making it clear he wants to join Pep Guardiola's side.
In addition, Wolves have agreed to sign City's England Under-21 international Tommy Doyle on loan, with the option of a £4.3m transfer that would include a huge sell-on clause for City.
These two deals are separate and come after City refused to meet Wolves initial £60m-plus valuation for Nunes.
City wanted to bolster their midfield options even before Kevin de Bruyne suffered the hamstring injury that could keep him out for four months.
West Ham's Lucas Paqueta was an option before it emerged the Brazilian, 25, is being investigated by the Football Association for potential betting rule breaches.
Wolves manager Gary O'Neil said after Tuesday's Carabao Cup win over Blackpool that he expected Nunes to stay at the club beyond Friday's transfer deadline.
The Midlands club signed Nunes on a five-year contract last summer, paying a club-record £38m to Sporting Lisbon.
He was a key figure during the second half of last season as Wolves successfully avoided relegation, finishing 13th in the table.
-- Courtesy of BBC Sport