The central midfielder has made 40 appearances for the Italian side this campaign and is developing into one of the most highly-rated Spanish stars.
However, it is said Napoli are now negotiating to extend his deal from 2023 by a further two years to 2025 and raise his salary to €5m per annum, putting him behind only Lorenzo Insigne and Kalidou Koulibaly at the club.
Interest from the Camp Nou is logical due to the uncertainty over the long-term futures of central midfielders Ivan Rakitic, Arturo Vidal and Sergio Busquets.
Fabian received his first senior Spain cap in June 2019 and has impressed in Serie A following a €30m transfer from Real Betis in the summer of 2018.
It was in Seville where the midfielder first truly came to prominence, under the tutelage of Quique Setien, and Diario AS reported earlier this year the midfielder would be a dream for the now Barcelona boss at the Camp Nou.
However, for now it appears that the midfielder is staying in Italy.