Gomez has nine goals in La Liga this season, but his club currently sit 18th in the table and four points from safety.
It is believed that the Uruguayan striker has a £50m release clause in his contract, but this would be halved if Celta Vigo are relegated this season.
According to Marca, Barcelona have been tracking Gomez for a long time and may meet his release clause this summer.
However, the report also claims that the Catalan giants would have to sell either Arthur, Malcolm or Vidal in order to free one of the non-EU player slots in their squad.
It was rumoured that Gomez was close to completing a £45m transfer to West Ham United in January, as Manuel Pellegrini searched for a replacement for Marko Arnautovic who was expected to move to China, before the deal fell through. body check tags ::