The Italian champions are in the market for a centre-back after the departure of Kim Min-Jae to Bayern Munich.
And Napoli have identified Wolves defender Kilman as the ideal replacement for the South Korean international.
However, the Serie A outfit failed with their initial bid of €35m for the centre-back and Wolves are adamant about not accepting any bid less than €40m.
Napoli, deeming Wolves valuation too high, stepped up their search for alternative targets.
Now, according to Italian daily Corriere dello Sport (via Calciomercato.com), they have reignited their interest in the Wolves star, but they still deem the price tag high.
It is said that Wolves are ready to offer Kilman a new deal and the 26-year-old is also not pushing for a move.
Now it remains to be seen whether Napoli will be able to come up with an offer to convince Wolves to let the player leave.