Barca have, however, refused to deviate from their £35m ($47m) asking price, leading to Marco Silva’s side to consider other targets.
With the Premier League transfer window due to close on August 9, time is running out for the Toffees to solve their defensive issues, and as such they are now looking at bringing in Rojo.
A deal for 23-year-old Mina may not be completely dead, however, and Goal understands Everton could be using interest in the Argentine as a tactic to hurry the Catalans towards a decision.
Lyon are also interested in the defender and are hopeful that the prospect of Champions League football could be sufficient to lure him to France , while the Ligue 1 outfit have time on their side with their transfer window not closing until the end of August.
There had been suggestions that Manchester United were themselves interested in signing Mina, but Goal understands that is not the case.
The player himself has, meanwhile, removed all traces of Barcelona from his Instagram account, having endured a frustrating six-month spell at Camp Nou.
Having only arrived from Palmeiras in January, he appeared only a handful of times for the first team under Ernesto Valverde.
The Frenchman underwent a medical on Tuesday, with the Toffees and Barca confirming a day later that the transfer had gone through.
Richarlison is another to have arrived in the summer window - the Brazilian netting on his debut last weekend as the Toffees went down 4-1 to Rennes in a friendly.
They are, however, poised for a flurry of activity in the final week before their season begins in earnest with a trip to newly-promoted Wolves.