United tabled the official offer to fight off moves by Everton and French side Lyon for the Colombia World Cup defender.
And the Old Trafford club expect Mina to pick them, despite a hold up when they pulled out in a dispute with his agent at the weekend.
Mina returned from holiday and thought he was signing for United on Sunday. But he found out that there was a snag and sought talks with his Barca bosses.
United turned up the heat in the race after failing to find an alternative and made one last and probably decisive play for Mina.
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The young centre-half will be offered a five year contract worth around £6million and has a chance to go into Jose Mourinho’s side.
United need a commitment quickly as they have an offer from Everton for Marcus Rojo on the table and will let him leave if a replacement comes in.
Mourinho wants solutions to his mounting problems and has made it clear that without new signings his side will fall by the wayside.
The Portuguese has bluntly demanded United get spending or let Manchester City run away from them again.
He told MUTV: "My CEO knows what I want and I still have a few days to wait and see what happens.
"The other clubs who compete with us are really strong and already have fantastic teams. Or they are investing massively like Liverpool, who are buying everything and everybody.
"If we don't make our team better it will be a difficult season for us."
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