The midfielder scored 11 goals in 37 games last season, helping his side to a third-place finish and Champions League qualification.
Coach Walter Mazzarri told Gazzetta dello Sport: "Marek is happy to work with me and he is very motivated.
"I have spoken to him and from what I know, he will not leave."
Napoli chairman Aurelio De Laurentiis recently put a €100m (£88m) price tag on the Slovakian.
Meanwhile, Arsenal chief executive Ivan Gazidis has suggested that the club are not finished with their summer spending after signing Lille striker Gervinho and Charlton Athletic left-back Carl Jenkinson for a combined £11.6m.