Since earning promotion to the Premier League, Wolves have been linked with a wide range of players, although managing director Laurie Dalrymple has suggested that the club are close to completing their business for the summer.
Wolves have pushed through deals for seven players - although Benik Afobe has already left for Stoke City - but according to The Mirror, the West Midlands outfit are prepared to pay a club-record fee for Zinchenko.
The 21-year-old enjoyed his breakthrough campaign with City last season, with the majority of his 14 appearances coming on the left side of defence due to the long-term injury of Benjamin Mendy.
However, the Ukraine international can also play in midfield and the player's versatility looks to have tempted Nuno Espirito Santo into giving Wolves the green light to spend in the region of £16m.
Should a deal be completed, Zinchenko would compete for the left wing-back spot with Barry Douglas and Ruben Vinagre, although Wolves are currently short on numbers in central midfield due to the exit of Alfred N'Diaye.