The Slovakian midfielder, who has scored 121 goals for Napoli during 12 seasons in all competitions, made his 520th appearance in Saturday's 3-0 win over Sampdoria.
"There are talks in progress and we are weighing it up together with the player," Ancelotti told reporters after the match.
"This club has great respect for this player, he has made history here, and if we wants a new experience, we are inclined to make it happen."
Hamsik, 31, joined Napoli from Slovan Bratislava in 2007.
He became the club's all-time leading scorer in December 2017 when he overtook Diego Maradona's record of 115 goals and he overhauled Giuseppe Bruscolotti's total of 511 appearances in November.
Hamsik was moved to a new position in front of the defence when Ancelotti replaced Maurizio Sarri as coach during the summer and has spent several matches on the bench this season as the squad has been rotated.
"Hamsik does not have a substitute in the squad but we have other players who interpret the role with different characteristics," said Ancelotti.
(Writing by Brian Homewood; editing by Clare Fallon)
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