Napoli are interested in bringing in a centre-back to replace Kim Min-jae, who has joined German champions Bayern Munich this summer.
Kilman has been Napoli’s top target and they failed with a bid worth €35m earlier in the transfer window.
The Serie A champions are yet to table a second offer but talks are ongoing in the background between all relevant parties.
And according to Italian daily Corriere del Mezzogiorno (via TuttoNapoli), Napoli have continued to try and convince Wolves to drop their asking price.
The Premier League club are not desperate to sell Kilman and will only consider offers worth €40m or more.
Napoli have not given up on Kilman and are expected to keep trying to convince Wolves to back down from their initial demands.
Wolves have already offered a new contract to Kilman and are prepared to dig in their heels if their asking price is not matched.
Napoli have other alternatives but they are not prepared to end their interest in the Wolves defender just yet.
