The Colombia international is expected to leave Barca this summer after a difficult six months in Spain.
The Catalans have keen to find a loan club for Mina, however Boca want to buy the defender outright.
Boca have offered €8m for Mina, with the deal including a hefty percentage of any sell-on fee. Barca are considering their response today.
Boca will be in Spain next month to meet Barca in the Joan Gamper Trophy.