The Daily Mail reports that United had a £15m bid for the 21-year-old rejected 18 months ago, but are now ready to re-ignite their interest in the midfielder.
Thiago has decided that it is time for him to leave Barcelona after having failed to become a first-team regular at the club.
"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."
Thiago has an £25million release clause in his current contract with Barcelona.