The Champions League title holders are banned from registering new transfers until January according to Sport.
Turan was expected to feature in the International Championship Cup and has been taken on the US tour by head coach Luis Enrique but he will only be able to train with the team.
The bearded winger arrived in Los Angeles with the rest of the team but suffered more bad news when he picked up an injury preventing him from joining team training.
The Turkish international joined Barcelona on a £24 million move from Atletico Madrid last month on a five-year deal.
Turan was closely linked with a move to United before joining Barcelona and Atletico Madrid CEO Enrique Cerezo claimed that the 28-year-old actually wanted to move to England.
Turkish newspaper AMK quoted Cerezo as saying: “Arda wanted to move to England but the transfer held commercial value. Arda is an idol in Turkey and some powerful groups wanted him at Barcelona.”
Turan was expected to join Premier League giants Chelsea or Manchester United following his agent Ahmet Bulut revealing he was in talks with three English clubs.
“He intends to leave Spain this summer. It is his will to go out to play in the Premiership, that is where he would like to continue his career at this time,” Bulut told AS.
“His departure from Atletico is not easy because he has a clause of €41m. There are ongoing talks with three teams at the moment. I cannot say their names, but they are the best of England and European football.”