Napoli have made signing a striker their No 1 priority this summer, but as yet they have only drawn blanks.
Trezeguet's agent Antonio Caliendo was asked by pensieroazzurro.com if his client would join Napoli.
"From what I know about the atmosphere and the warmth of the city and the fans, I am optimistic about a solution for David involving Napoli.
"Right now I am in Milan. I haven't yet spoken to Napoli's director of sport about Trezeguet, but if he were to contact me I would be open to talks."
Caliendo was then pressed on whether he had spoken about Napoli with Trezeguet.
"Yes, I have exchanged a few conversations with him on this team. David asked for information about the place and I tried to make him understand about the love of Napoli's fans and the warmth that they manage to transmit to those players who wear the blue shirt.
"I believe that if Napoli were ask me, David wouldn't be unhappy with the prospect of playing for them.
"We are in talks with Valencia. Three days ago I received a written offer from Turkey and the United States. But a fundamental aspect for the player is the chance to be close to his family.