Wolves have been following Kessie since the end of last season and made an attempt last summer. Molineux chiefs are ready to try again in January.
However, MilanNews says West Ham are also in contact about bringing the youngster to England.
Both Premier League clubs are willing to offer €20-25m to convince Milan to sell.
For his part, Kessie will be tempted by a move to England, particularly as he battles to win over new Rossonero coach Stefano Pioli.