Premier League duo Chelsea and Manchester United have been linked with the 26-year-old Slovakian, who has seen high-profile teammates such as Ezequiel Lavezzi and Edinson Cavani leave the San Paolo in recent seasons.
The Partenopei chief, however, denied such claims, telling Radio Kiss Kiss: "It's only journalists who put him on the market.
"Marek has to come and tell me if he wants to go, but there is no more Neapolitan player than him. He has become Neapolitan and for me he is absolutely not for sale.
"Of course if he came to me and asked to leave, then we'd have to discuss it."
Hamsik is currently in his seventh season with Napoli.