Talks are at an advanced stage with 21-year-old AC Milan and Italy forward Cutrone, who left Milan's pre-season tour of the USA early to return home ahead as he prepares to leave the club.
No deal has been finalised yet but it's reported that Wolves will pay £16million up front for the 6ft striker, plus £4m in add-ons, and offer him a five-year contract.
Cutrone scored 16 goals in 42 games in his breakthrough season in 2017/18 before netting nine in 43 last year.
He is seen as an ideal alternative to Raul Jimenez and Diogo Jota and is described as a classic number nine with a strong work ethic and good aerial ability.
Wolves still harbour hopes of signing both Cutrone and Benfica defender Ruben Dias, although a deal for the latter is thought to be 'complicated'.
It's believed the 22-year-old centre half is interested in a move to Molineux but Benfica are desperate to keep Dias, who has been capped 11 times by Portugal.
They have been in negotiations over a new contract for some time, with Dias' existing deal including a £57million release clause.
The 6ft 1in player's agent is Jorge Mendes, who has close links to Wolves and has brokered a number of deals for the club in the past three years.
Dias is Wolves' number one choice and they will continue to pursue him despite signing fellow defender Jesus Vallejo on a season-long loan from Real Madrid yesterday.
They have a shortage of specialist centre halves, with Leander Dendoncker now firmly classed as a central midfielder and Romain Saiss having not been able to cement a place when being given a run in defence towards the end of last season.
It's believed that despite widespread reports, there is no substance to links with Dinamo Zagreb's Spanish attacking midfielder Dani Olmo.