The Uruguayan striker is said to have a release clause of £44m and a contract with Celta until June 30, 2022.
West Ham is said to be exploring a number of possibilities to prepare for a possible departure of Marko Arnautovic, who is subject a bid from a Chinese Super League club thought to Shanghai SIPG for £31m.
Gomez has hit 26 La Liga goals in 50 starts since joining from Defensor Sporting in a €4m deal in 2017. He has scored eight goals this season, half of what he managed last season in 36 matches. Pellegrini is likely to have drawn up a list of possible striker should Marko Arnautivic and/or Javier Hernandez this January.