The Daily Star says United will pay Barcelona around £17m for the 22-year-old midfield ace.
Thiago lit up the European Under-21 Championship and captained Spain to glory.
He netted a hat-trick in the final against Italy which sparked United into action.
Barcelona were keen for Italian-born Thiago to stay and team-mates Gerard Pique and Xavi both told him to not to leave the Nou Camp.
But the ambitious star met club bosses to inform them that he wanted to join United.