The 21-year-old Ivory Coast international has impressed during his time at the San Siro, having joined in June 2017 on a two-year loan from fellow Serie A side Atalanta. The loan deal contains an obligation to buy.
Kessie made 54 appearances in all competitions for Milan last season, scoring five times. He also provided three assists during the season.
Milan boss Gennaro Gattuso, who was an impressive midfielder himself during his playing days, said the youngster was "far better than I ever was", in quotes reported by Mediaset.
Since making his senior international debut in 2014 aged 17, Kessie has gone on to win 21 caps for his country, but has yet to score at international level.
One potential stumbling block for a move to Wolves though is that the player is said to be content at Milan and not interested in leaving the Italian club. Kessie is currently under contract until 2022 but is said to be interested in signing an improved deal to further commit his future to his current club.
Wolves have been very ambitious this summer with their transfer business, but it appears as if the potential transfer of Kessie to Molineux may allude them.
Kessie is the second talented young Milan player Wolves have look to sign this summer, having also seen their interest in 22-year-old Portuguese forward Andre Silva - who struggled at the Rossoneri last season.
Silva is a client of agent Jorge Mendes, who has close links with Wolves and orchestrated many of the club's recent high-profile moves, but is also attracting interest from larger European clubs like Sevilla.