Hamsik is under contract with Napoli until June 2016.
"My desire is to remain and win with the Napoli jersey," Hamsik said to Italian newspaper Il Mattino.
Reports in Italy claimed Hamsik, who has scored nine goals in 36 league appearances for Napoli, could leave the San Paolo stadium this summer if his club fail to qualify for the Champions League next season.
Napoli are three points behind Udinese, who hold the last Champions League qualifying spot heading into the final weekend in Serie A.
The Naples outfit must beat Siena and hope Udinese lose and Lazio fail to win their respective games in order to finish in the vital third position.