Turan missed several days of training after picking up a foot injury according to Marca but joined the team in their third training session at the Cox Stadium in San Francisco.
The bearded winger will not however, be able to play against United due to the FIFA transfer ban.
The Turkish international was expected to feature in the pre-season but the transfer ban also applies to friendly games.
Barcelona can sign players but cannot register them until at least January. Turan will not be able to play a professional game for the La Liga champions until the new year.
The Champions League title holders beat La Galaxy in their first International Championship Cup game and will take on United next before facing Chelsea in the final group game.
United and Chelsea were both closely linked with Turan before his move to Barcelona. The Turkish international did want a Premier League move according to his agent Ahmet Bulut who admitted being in talks with three English clubs but the deal fell through.
“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.”