The Blaugrana are set for major changes ahead of the 2020-21 season following their 8-2 Champions League humiliation against Bayern Munich.
The Catalan giants need to drastically reduce their wage bill and also reduce the average age of their squad, so the 33-year-old central defender could be one such player who could exit the Camp Nou this summer.
Diario Sport have cited a report from Libero that the central defender is a transfer target for the West London club, who won promotion earlier this month via the promotion playoffs.
The report highlights how Pique himself has even offered to leave Barca should it help the club, with the club already having players like Clement Lenglet, Samuel Umtiti and Ronald Araujo in the position, while they have also been linked with a summer move for Manchester City defender Eric Garcia.
Pique had a stint in England previously with Manchester United, but it remains unlikely that Fulham would be able to fund a move this summer.