According to Marca, super-agent Jorge Mendes told Barça about the offer, the same figure that they paid Valencia for his signature after a triumphant Euro 2016. But the response was negative and the official line would appear to be that the player is not for sale.
It is said that new Barcelona coach Ernesto Valverde and the Camp Nou hierarchy wish to keep hold of 23-year-old Gomes, despite his failure to so far justify his place at the club, in a bid to ensure that the squad is not left under-resourced ahead of next season.
Even if top midfield target Marco Verratti were to arrive from Paris Saint-Germain, Marca notes that the more attacking Gomes would not be in direct competition with the Italian for a place in the team and therefore isn't under any immediate pressure.
It remains to be seen exactly which English club made the alleged offer for Gomes.
Manchester United have been linked with a move as a result of the connection between Mendes and Jose Mourinho, one of his most high profile clients.
Mundo Deportivo, however, claims that not just one but three offers for Gomes have been made and rejected. The Catalan publication specifically names Manchester United, as well as Arsenal or Tottenham - but they seem very unsure over which north London side it could be.
The third offer is supposed to have come from Juventus, a club that was heavily rumoured to be chasing Gomes before he chose to join Barcelona last year.