Sunderland are reportedly hoping to strengthen their squad in the January transfer window.
The Black Cats have realised their need to strengthen if they are to escape the drop this season, and they feel that January could be a crucial month for them.
As a result, Sunderland are already starting to formulate plans for the next transfer window, and tightening up their defence has become a priority.
The Black Cats have let in 16 goals in their first seven Premier League matches, but they reportedly feel that Gomez would improve their squad.
The 23-year-old has impressed in La Liga and, having been developed at Barcelona, he is very comfortable in possession.
Sunderland manager Dick Advocaat has told the Sunderland Echo that all his defenders are too keen to just kick the ball away, and it could be that Gomez is the assured defender that he is searching for.
Gomez has made three appearances for Celta this season, with the Spanish side currently sitting in fourth place in La Liga table.