United have been keen on the Spain international for the past three years and had a £15million bid rejected 18 months ago.
The 21-year-old was determined to establish himself in the first team set-up but now has accepted it is time to move on.
"My son would play a lot more in any other team in the world," said his father Mazinho. "He’s learning a lot playing with great players but Thiago is very ambitious and needs to play.
"No-one knows what might happen in the future. Football changes a lot and anything can happen. If Thiago wants to go to the 2014 World Cup, he needs to play much more.
"Thiago has the quality to succeed at Barca. But he’d play a lot more at another club. He’d get into any other team in the world.
"I don’t know if Barca are buying more players in the summer. They already have a lot of players who can play in the middle. Also, [his brother] Rafinha will be part of the first team squad next season."
Is Thiago good enough to break into United's midfield? Give us your shout below...