The 23-year-old arrived at Barca from Palmeiras in January, but the Camp Nou side have already decided to listen to offers for the Colombian defender despite his bright World Cup campaign and insistence that he wants to stay.
The Premier League outfit were told to return with a better bid amid further offers from West Ham, Borussia Dortmund and Lyon, whose president claimed Mina preferred a move to France over one to Merseyside.
But just a day after seeing Barca beat them to the signing of Malcom from Bordeaux, the Toffees are confident of wrapping up the signing of the defender after submitting an offer worth £27m, which the Catalan club are ready to accept.
The Blaugrana will make almost three times the figure they paid to bring Mina to Camp Nou, but are not willing to cut ties with him completely as they will insert a buy-back option in the deal.
Mina is a top target for new Everton boss Marco Silva, who has already held talks with his uncle and representative, Jair Mina, over the centre-back's role in the team.
Mina signed a five-and-a-half-year deal with Barca in January, but made just six appearances for Ernesto Valverde’s side as they went on to win the Spanish league title.
However, the arrival of Arthur Melo from Gremio this summer forced Barca to consider letting him go due to having too many foreign players.
Mina has 15 caps for Colombia to his name and took his goal record for the national team up to six with his key role in their World Cup campaign.