The Colombian centre-back has seen stock rise following his showing at the World Cup in Russia, despite his playing time being limited at club-level with Barcelona.
Mina admitted earlier in the summer that he had received offers to leave Camp Nou but would prefer to stay at Barca and win over head coach Ernesto Valverde.
Goal understands that the 23-year-old is ready to make a move to the Premier League with Everton, and that the club have already been informed that he was content with their offer through his uncle and representative Jair Mina.
Everton coach Marco Silva contacted Jair Mina to explain his project at Goodison Park and the role he sees the 23-year-old defender having in his squad, where he would have the chance to be a regular starter, as opposed to his position with the Spanish giants where he would likely see little time on the pitch.
The only sticking point now is the approval of a deal from Barcelona.
Everton have offered the Catalan club €17 million (£15m/$20m) plus add-ons. Mina joined Barca from Palmeiras for €11.8 million (£11m/$14m) in January, meaning Barcelona would turn a tidy profit on the deal.
The Spanish side would also want to keep a buy-back option on the Colombian.
Negotiations with Barcelona are being commanded in person by Everton sporting director Marcel Brands and he is optimistic that it will have a positive outcome for the English team when Mina returns from his post World Cup.