Alba's future with Ronald Koeman's side is currently being called into question, with Inter Milan said to be showing an interest in the Spain international.
According to Mundo Deportivo, should the experienced left-back move on during this summer's transfer window then the Catalan giants will attempt to sign Gaya as his replacement.
Gaya, who scored once and provided seven assists in 33 La Liga appearances during the 2020-21 campaign, is believed to have halted contract talks with Valencia.
The 26-year-old only has two years left to run on his current deal at Mestalla and is believed to be a long-term target for Barcelona.
Alba's understudy at Camp Nou, Junior Firpo, could also be on the move during this summer's transfer window, with AC Milan thought to be showing an interest.