Mina joined Barcelona from Palmeiras during the January transfer window, and made six appearances for the Catalan club in the second half of the campaign.
Barcelona have since brought Clement Lenglet to Camp Nou, however, and it is understood that Mina could be available for transfer.
Jair Mina has confirmed that he has held talks with Everton over a move to the Premier League, but has conceded that the centre-back is keen to stay at Barcelona.
"I've spoken to Everton's director of football (Marcel Brands). Yerry has lots of offers to leave but his dream is to play for Barca," Jair Mina told Esports Cope.
"He knows that Barca have 25 squad places available and everyone is important. But what's important to him is that he plays. We won't do anything unless Barcelona tell us that we need to find a new club for Yerry."
Mina, who impressed for Colombia at the 2018 World Cup, recently revealed that he was determined to 'succeed at Barcelona'.