The Daily Star says Barca were reluctant to sell one of their rising stars, with club official Andoni Zubizarreta working overtime in a bid to talk him into staying at the Nou Camp.
But the 22-year-old has decided he will not play enough games with the Spanish champions.
David Moyes has told Alcantara he will be a major influence in his team, persuading him to join the Premier League champions.
Alcantara is desperate to make the Spain squad for next summer's World Cup in Brazil.
And he thinks establishing himself with United will help him achieve this.
A source said: "Thiago is frustrated because he knows his opportunities at Barcelona are limited.
"Joining United is a fresh challenge and if he will be getting regular games there is no reason why he won't be involved in the World Cup.
"He also knows United are such a massive club and one that can match his future ambitions."
United are hoping to unveil Alcantara next week after the deal has been finalised.