West Ham are looking to add another midfielder.
Gomes is a central midfielder who signed from Valencia a year ago, who he previously joined from Benfica.
The 24-year-old would be an alternative to his Portugal international colleague William Carvalho.
Gomes failed to win over Barcelona fans last season and finds his place at the Nou Camp under threat from new signing Paulinho.
The defensive midfielder is potentially a long term replacement for Mark Noble at West Ham.
Slaven Bilic's side have bought well this summer but have lost their first two Premier League games, and are still looking for fresh faces to give the squad a boost.
He only managed to make 17 La Liga starts, with a further 13 appearances from the bench, scoring three times and providing one assist.
Gomes started the first leg of Barcelona's Spanish Super Cup loss to Real Madrid and was not picked for the second.