Anguissa joined the Serie A club last summer on a season-long loan and as part of the deal Napoli have the option to buy the midfielder.
The Cameroonian has impressed for Napoli and has become a fan favourite at the club as they make a challenge for the Serie A title.
Napoli are happy with him and are willing to sign the player permanently after the season ends, but things are not straightforward.
The Napoli board are hoping that Fulham budge from their price and they are able to sign the midfielder for a discount, according to Italian daily Corriere dello Sport.
Before sending him out on loan in the summer, the London club got Anguissa to sign a three-year contract with them.
It is claimed that Fulham are still not settled on the future of Anguissa and are contemplating calling him back to their ranks as they are favourites to achieve promotion to the Premier League.
Anguissa has made 23 appearances for the Naples club this term, despite having injury troubles, and is keen to stay in Italy with the Serie A giants.
