The Serie A champions have identified Kilman as the potential replacement for Bayern Munich-bound Min-jae Kim.
Napoli have already failed with a bid of around €35m for the Wolves defender and are now mulling over their next steps.
Wolves are prepared to sell him but want a deal worth €40m before agreeing to let the player go in the ongoing transfer window.
Napoli are still very much in the race and according to La Repubblica (via TuttoNapoli), they have been in touch with his representatives.
The Serie A giants are planning their next course of action with Kilman’s agents as they seek to sign the centre-back this summer.
The defender also has suitors in the Premier League where West Ham are believed to be interested in him
Wolves and Kilman are not desperate to part ways yet and he is likely to be offered a new contract if he stays.
However, Wolves are likely to sell if they receive an acceptable offer for him in the current window.
