The report in talkSPORT claims the Slovakian star is prepared to commit his future to the Serie 'A' club, amid speculation that several of Europe's biggest names could be poised to make a bid for the Napoli midfielder.
Chelsea and Manchester City have been linked with the 25-year-old on several occasions over the past 24 months, but Juraj Venglos, the player's agent, has insisted Hamsik will not be moving.
Speaking to Italian radio station CRC, Venglos said: "His dream is to play regularly in the Champions League, and with Napoli that is possible.
"We are currently studying the club's offer and he could stay in Naples for life.
"He could become captain and that would be a privilege, and to leave is not part of his plans."
Hamsik has been one of Napoli's best players over the past two years, along with in-demand striker Edinson Cavani.
His performances in southern Italy have attracted interest from across Europe, but it now seems Chelsea and Manchester City will miss out on the midfielder. Cavani and Hamsik have been key to Napoli's fortunes in recent seasons, and both are highly rated by the Naples board.