Gomez, 21, is considered to be a bright midfield prospect and Inter Miami are expected to struggle to hold on to him this summer.
He is a player that West Ham rate highly and the Hammers have been tipped to be firmly in the mix for his signature.
They now face serious competition from Brighton though as the Seagulls have sent an offer to Inter Miami for Gomez.
Brighton are not the only club to have put in a bid for Gomez and it is unclear what level the offers on the table are at, or whether West Ham are one of the other sides to have bid.
Gomez has been out through injury, but is now back in training, and he is expected to represent Paraguay at the Olympic Games.
It has been suggested that Gomez’s future is only likely to be clarified following his participation in the Oympics.
Brighton though have put their cards on the table now and signalled their desire to take the midfielder to the Premier League
