Genk have yet to receive an offer for the 21-year-old, but the highly-rated central midfielder looks set to depart with only 18 months left on his current contract.
The club's sporting director Dimitri De Conde stated recently that there is wide interest in Berge from Serie A clubs as well as the European champions.
"Napoli are interested in Sander, it's a possibility a deal could be done,” De Conde told Radio Punto Nuovo. “We also know that Liverpool are interested and [Jurgen] Klopp, after the game at Anfield [in the Champions League], complimented him on his performance.
“There are clubs in Italy who are following Berge and Napoli could be one of them, but at this stage, there are no offers on the table. From next week, things could change. We haven't had any official contact with Napoli yet.”
Genk maintain a close connection with Chelsea having agreed sales for both Kevin De Bruyne and Thibaut Courtois in the recent past.
Berge, who has 20 caps for Norway, is the Belgian club’s brightest talent and has had experience in the Champions League. He has faced Liverpool and Napoli already this season, admitting over the international break that a move to Jurgen Klopp's side would be a dream come true.