Gaya has made 275 appearances for Los Che, including 14 outings in all competitions during the current season.
Alba remains a key player for Barca, making 18 appearances this campaign, but the Catalan giants are said to be preparing to sign a replacement.
According to Fichajes, the Blaugrana are keen to sign Gaya, who could be the perfect player to take Alba’s position on a long-term basis.
The report adds that Valencia want €50m for the 26-year-old, but the Spanish outfit are not in a strong position to negotiate, with his current deal due to expire in June 2023.
Barcelona are also close to reaching an agreement with Chelsea’s Andreas Christensen on a free transfer.