He has been hailed as the new Ronaldinho and his club have just turned down an £8million bid from Villarreal for his services.
United have been monitoring Costa through their South American scout - former centre-back Jaap Stam.
Costa would not need a work permit to move to England because he has a Portuguese passport.
Chris Nathaniel, Costa's advisor, said: "The boy is special and loves the Premier League. He has a lot of offers to consider."