The 21-year-old Italian international is available, with Milan reportedly trying to free up funds to buy Angel Correa.
And the Express & Star understands that Wolves are in a great position to land the 6ft striker, who scored seven goals in the opening 16 games of last season for the Italian giants.
Cutrone's goalscoring form tailed off after that, with him netting only twice more for the remainder of the campaign, but Wolves see huge potential in the Como-born front-man and believe he offers a quality alternative to Raul Jimenez and Diogo Jota up front.
Talks are at an advanced stage and it's understood Wolves believe the deal can be done.
Reports in Italy have suggested Milan wanted £22m for Cutrone, but it's understood the fee is lower than the figures quoted.
Cutrone played for Italy throughout the youth levels and earned his senior debut in March 2018 against Argentina, his only cap to date.
After coming through the ranks at Milan he made his debut aged 19 on the final day of the 2016/17 season. He then scored in the first two Serie A games of 2017/18, going on to score an impressive 16 goals in 42 games that season and then nine in 43 last season.
Wolves have yet to sign a 'new' player this season, with the £32m and £12m captures on loan players Jimenez and Leander Dendoncker their only senior signings to date.
Nuno Espirito Santo said this week the club certainly needed new players. They have only 12 senior outfield players out in China for this week's Premier League Asia Trophy tournament.
It's believed club bosses are also chasing a centre half and possibly a midfielder as they look to bring in three or four quality first-team additions this summer.