Everton had been seeking to sign a new centre-back on deadline day, with Mina their top target.
Jose Mourinho has made no secret of his frustration at United's transfer business this summer as Brazilian midfielder Fred has been the only significant addition so far with Lee Grant arriving as a third-choice goalkeeper while Diogo Dalot is a young full-back for the future.
Everton have been chasing the 23-year-old since his impressive World Cup exploits.
"The Club reserves the right to buy back the player".
Mina - and his teammate Andre Gomes - supposedly had medicals in Barcelona today ahead of their proposed moves away from the Nou Camp.
With the ability to play at centre-back or at full-back, he'll provide a decent option to Marco Silva if a deal is completed before the transfer window closes.
The Everton manager also let Ashley Williams leave the side on loan to join Stoke City and Ramiro Funes Mori was allowed to join Villarreal.
The Toffees face Wolves on their opening day of the season on Saturday (5.30pm) before a clash with Southampton a week later.