The Toffees have offered €24m (£21m) for the Colombia international defender, Goal.com reports.
Negotiations between the clubs are said to be underway, but Barca's terms could prove to be a stumbling block.
According to the report, the Catalan giants were initially keen to send Mina on loan to Everton, but could be willing to sell him if they are granted a buy-back option.
Everton reached a similar agreement with Barcelona over Gerard Deulofeu several years back, signing him with a buy-back deal in place which Barca took advantage of in 2017.
Mina, who scored three times at the World Cup, has also been linked with Everton's local rivals Liverpool.