The German coach says medical staff will continue to evaluate the striker's hamstring injury but he refused to speculate on whether he could face Portugal
Altidore pulled up with a hamstring issue early in the 2-1 victory on Monday over Ghana and was carried off on a stretcher as young forward Aron Johannsson replaced him.
Altidore had an MRI scan on his injured left leg on Tuesday in Sao Paulo to determine the extent of the damage and Klinsmann remains optimistic he could yet play a further part in the tournament.
"We have to see how he reacts in the next couple of days with his hamstring, and we are full of hope that he comes back still in this tournament," Klinsmann said. "That's what we are going to work on every day.
"The medical staff has done a tremendous job. We still have hope that Jozy will come back. How quickly? That is down to his healing process."
USA take on Portugal in Manaus on Sunday in the second round of group-stage fixtures.