Adu, 17, was allowed to attend by MLS club DC United, but will not be able to play in a competitive match as he does not have a work permit.
Chelsea are reported to have rejected the chance to sign Adu, who is the youngest-ever USA international.
Despite his reputation, Adu trained with United's academy players at their Carrington training ground.
Ghana-born Adu was 16 when he made his international debut for the USA in a friendly against Canada.
United are thought to be keen to arrange a match behind close doors at some point during Adu's stay.
Earlier this month, boss Sir Alex Ferguson confirmed United would be keen on signing Adu if he could prove himself.
Ferguson said: "I think we would be interested, he's only young but we have known of him for a long time.
"We tried to get him here some years ago but he signed for DC United and that stopped the progress of us keeping tabs on him."
Earlier this year Adu's agent Richard Motzkin claimed he had held talks with both United and Chelsea.