Gomes and Ronaldo are close - something which has often irked Lionel Messi - because of their national allegiance.
Barca are already making plans for January but they are hoping to land a creative spark and a defender - with a striker also on the agenda.
But to have to replace a squad man in midfield would complicate things.
Gomes, though, wants to quit the Nou Camp next month and has interest from Juventus.
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Barcelona paid £30m for him in 2016 when they signed him from Valencia.
Valverde would sanction a departure but only for a fee where he could replace him with a player of similar quality.
Barcelona are keen to strengthen in January despite a decent start to the season.
They face Chelsea in the last 16 of the Champions League after winning their group and lead La Liga by five points.
Rivals Real Madrid are down in fourth, eight points back, after 15 games.