The Colombia international has been seeking a move away from the Liga champions all summer after a disappointing time at the club following his January arrival from Palmeiras.
Mina failed to break into Ernesto Valverde’s plans, playing just five times in the league and has since been allowed to seek a move elsewhere in the summer window.
Despite a strong World Cup performance that saw him score three goals in Russia, the defender has been pushed further down the Barca pecking order with the arrival of Clement Lenglet.
A move to Everton had originally appeared to be in the cards, but Mina then emerged as a target for Manchester United as the Red Devils looked for an alternative to expensive targets Harry Maguire and Toby Alderweireld.
However, Goal understands United have pulled the plug on a move for Mina, focussing their attentions on landing Alderweireld instead.
While that would appear to clear the way for Mina to move to Everton, it is also understood that the Toffees are now not interested in re-entering negotiations for the centre-back.
Marco Silva's side have been frustrated over the way they have been dealt with in the negotiating process, feeling that they were used and then discarded when United's interest emerged.
With the two Premier League clubs having rescinded their offers, it now leaves Mina with no suitors at the current time.
A move to England would have to materialise in the next few days, as the Premier League transfer window closes on August 9.
However, that would not necessarily end the chances for Mina to find a new home as most other leagues have a later transfer deadline, with a move still possible elsewhere until August 31.