The defender has a release clause of €50m in place on his contract at the Mestalla but the club are likely to be open to negotiating far below this amount due to financial pressures of missing out on European football.
The details are outlined by a report in Diario Sport, who say that the player is one of the club’s three priority signings this summer along with Inter striker Lautaro Martinez and Manchester City defender Eric Garcia.
Those three players are likely to dominate Barcelona transfer news this summer, although it is acknowledged that the club must sell several first-team players first before investing.
The news comes amid reports that Jordi Alba is one of the starting players who the Blaugrana will consider selling this summer, with Junior Firpo’s future also in question.
Gaya starred for Spain’s Under-21 side in the 2017 European Championships and has gone on to win seven caps for the Spain senior team, scoring once and becoming a fixture in Valencia’s first team.
Gaya has made 227 first-team appearances at the Mestalla and become one of the club’s star players in recent seasons.