The Azzurri are currently on the lookout for help in attack after star striker Edinson Cavani was sold to Paris Saint-Germain for €64.5 million.
As a result they have been linked with a move for multiple strikers in recent weeks, with Quagliarella and Gilardino being thrown about as possible targets.
However, Genoa president Enrico Preziosi poured cold water on a possible move for Gilardino.
“Gilardino to Napoli? I’m not aware of that,” he told Tuttomercatoweb.com.
“I’ve had no contact with Napoli and therefore I can say that there has been no official offer made for Gilardino.”
Elsewhere, Napoli owner Aurelio De Laurentiis refuted the Quagliarella rumour by responding with a resounding “no” when asked by a fan on Twitter regarding a possible return of the Naples native.
The Partenopei have already signed forward Jose Callejon, previously of Real Madrid, in this summer transfer window and look set to wrap up a deal for fellow Spaniard Raul Albiol in the coming days.