Gazzaniga spent last season on-loan with the Segunda Liga outfit, where he enjoyed an outstanding campaign.
The Argentine has returned to St Mary's, where his future will now be decided by new manager Mauricio Pellegrino.
Rayo have already made it clear to Saints they'd be happy to take Gazzaniga on a fresh deal next term.
Michel, Rayo's coach, said of the keeper: "I love his commitment. He arrived as an outsider, but became a heavyweight of the dressing room. In addition to his talent, he is a leader."