Mina celebrated keeping Everton in the Premier League on the final day of the season but has announced that he will be leaving the club this summer.
His current deal expires at the end of next month and the centre-back is available on a free transfer.
The centre-back’s agent has been fielding calls from several clubs in Europe but Besiktas are pushing to get a deal done soon.
According to Turkish outlet Fotomac, the Istanbul giants have been in contact with his representatives over a potential deal.
Besiktas have conveyed to the player’s entourage that they want to hold face-to-face talks with his agent.
The response from Mina’s camp has not been negative and his agent is now trying to convince the player to consider a move to Turkey.
The Colombian is a top target for Besiktas and they are aware of the competition they are likely to face due to his free-agent status.
They want to wrap up a deal to sign him soon in order to beat the competition to his signature.