The American forward sustained a hamstring injury in the first group match but could return for the round of 16 match.
The forward has been unable to play since he pulled up with a hamstring injury while chasing a long ball in the Americans' tournament-opening victory against Ghana. Altidore traveled but did not dress for group matches against Portugal and Germany as he recovered.
The 24-year-old started running during training again last week and participated in the open portion of Monday's session.
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Clint Dempsey has played as the lone striker in the Sunderland man's absence, but while Dempsey has performed well, Altidore's athleticism and physicality has been missed by Jurgen Klinsmann's side.