The Hammers reportedly led the way to sign Gomez during the January transfer window. The 22-year-old has scored nine La Liga goals and contributed five assists in 25 games this season.
Unfortunately, Celta's campaign has been a largely miserable one. They have taken one point from their last six games and now find themselves in the relegation zone with 10 fixtures remaining.
Celta being relegated will surely make it easier for Gomez to seal a move elsewhere. But The Sun reports that that is the scenario that the Irons are concerned about with his release clause set to become £21.3 million rather than £42.6 million.
The Sun suggests that that drop in price is likely to see the competition for his signature increase significantly, with both Liverpool and Chelsea apparently monitoring the youngster.
The Hammers may not be able to compete with some of their rivals financially when it comes to the contract they can potentially offer Gomez. But what Manuel Pellegrini's men can provide is a greater chance of regular game-time for the striker.
West Ham have done well this year, and look to be on course for a top-half finish in the Premier League. But there is arguably still an opportunity for a striker to establish themselves as first-choice in the Irons lineup with their top goalscorer this term boasting eight league goals.
Convincing Gomez to turn down the opportunities that allow him to play European football will be tough. But West Ham have pulled off plenty of transfer coups in recent years, so perhaps they cannot be ruled out of the running just yet.