The 23-year-old only moved to the Camp Nou in January following an impressive two-year spell with Brazilian side Palmeiras, joining the Blaugrana for just over £10m.
But Mina has struggled to settle in Catalonia, making just six appearances across all competitions after putting pen to paper on a five-and-a-half-year contract with Barcelona, failing to make an impression on the club's hierarchy and supporters.
Despite his impressive displays at the World Cup this summer, La Liga champions Barcelona are still keen on cashing in ahead of the new campaign, something which has attracted the attention of a number of top clubs from across Europe.
And a report from Goal claims that Everton are closest to reaching an agreement for Mina's signature, with the defender set to cost the Toffees roughly £21m.
Would love us to sign Yerry Mina purely so that him & Tom Davies can have a great game together & the headline in the paper the next day could be ‘The Tom & Yerry Show’.— UpperGwladysBlue (@UpperGwladysBlu) July 10, 2018
It is added that the expected arrival of Sevilla's Clément Lenglet has persuaded Barcelona into selling Mina this summer, although the club are demanding that they retain a buy-back option in his contract at Goodison Park.
Director of football Marcel Brands has already held talks with officials at Barcelona ahead of the move, with manager Marco Silva equally keen on adding Mina to his squad ahead of the new Premier League season.
Everton are yet to make any signings this summer, although the likes of Sandro Ramírez and Ademola Lookman have returned from loan spells away from the club. Promising winger Henry Onyekuru will be forced out on loan again due to issues with a work permit.