Wolves have already allowed Ruben Neves and Danny Collins to leave the club this summer, but they are desperate to keep hold of Max Kilman.
The defender has been attracting interest from Italy throughout the transfer window, with the Premier League having already turned down a bid worth over $30 million.
Wolves hoping to agree on new Max Kilman deal
The Premier League side have been forced to offload a number of key players this summer due to FFP regulations, but there is a belief that there is no longer a need to sell players following the departures of Neves and Collins.
Wolves will now look to tie down one of the best performing defenders over recent seasons by offering Max Kilman an improved long-term deal to stay in the West Midlands.
However, Napoli remain keen on increasing their offer, and could return with a fresh move for the central defender, according to the Telegraph.
Julen Lopetegui is hopeful of keeping hold of Kilman, who has played 107 times for Wolves since joining the club from Maidenhead United in 2018.