The Gremio midfielder, 18, was arrested by Brazilian police earlier in the week for driving without a valid licence. He has already been fined by police and has had yet another dressing-down from club officials.
It is the latest incident in his controversial career and Manchester United have been made aware of an increasingly long list of off-field problems.
Costa, who does not drink, has already been criticised by his coach for his party lifestyle and is frequently late for training.
Boss Fergie is unwilling to meet the £18million buy-out clause in his contract, which runs until 2013. United have offered just short of £7million.