Ex-Bolton misfit Dzemaili is understood to be keen to have another crack at the Premier League.
His first spell in England ended badly as he managed just once substitute appearance in two years at the club, having suffered a string of injuries.
But Newcastle will have to fend off German duo Borussia Monchengladbach and Stuttgart if they want to land the midfielder.
His four goals in the group stages of the Champions League propelled Napoli to a last-16 tie with Chelsea and they currently lead 3-1 after the first leg in Italy.
Dzemaili has a contract at Napoli until 2015 but Newcastle are ready to test Napoli's resolve with a summer bid for the Switzerland international.