Mertens, 28, has made just five Serie A starts for Napoli this season, sparking speculation that he could be on the move this summer.
Liverpool had registered an interest in Mertens back in January but held off from making a bid until the summer, with Napoli more likely to listen to offers in June.
However, according to TMW, Mertens has instigated talks with the club about extending his current deal, which expires in 2018.
Napoli have all but secured an automatic place in next season’s Champions League and are determined to keep their squad together for their return to the competition.
Despite being used mainly as a substitute in the league, Mertens has still managed to find the net 11 times for his club this season and scored a hat-trick against Bologna last night.