The 24-year-old, who had been linked with a number of European clubs following his impressive form this season, has signed a contract extension that will keep him at the Stadio San Paolo until 2016.
"I have renewed my contract because I believe in Napoli and because I feel fine here," Hamsik told Sky Sport Italia.
"If I prefer to win the Coppa Italia to finishing third in Serie A? I do not rule anything out, we are playing for both things.
"It is a shame that we crashed out of the Champions League, but we did well and we want to continue like this."
The side will visit Roma on Saturday in their next Serie A game.