The 23-year-old joined the Spanish club in the summer and has impressed after scoring five LaLiga goals already this campaign.
According to Calciomercato, the Black Cats are now apparently weighing up a move in January for the Romanian.
David Moyes is keen to add some firepower to his side and ease the goalscoring burden on 34-year-old Jermain Defoe.
As well as Andone, Sunderland are also reportedly tracking FC Copenhagen striker Federico Santander.