The Hammers had an £18m bid for the Portugal international turned down by the La Liga champions last week.
The report claims that West Ham have submitted a new bid for the classy midfielder in the region of £20m, although Barcelona are demanding a fee between £25m and £35m.
The 25-year-old impressed last season on loan at Everton, where he made 29 appearances.
Bolstering the midfield is one of Manuel Pellegrini’s top priorities this summer, and Gomes has emerged as the club’s top summer target.
Thankfully, the Hammers won’t have to pay that much, and it remains to be seen whether their second offer is enough to secure his signing.
Gomes made 78 appearances during his two seasons with the Catalan club, helping them win the La Liga title in 2018.