Neuer, 40, is currently nursing a left calf injury that disrupted the end of his Bundesliga season with Bayern Munich. The problem also ruled him out of Germany's two most recent warm-up matches.
However, the veteran shot-stopper has since recovered enough to return to individual goalkeeper training and is expected to start for Germany in their upcoming matches, provided there are no further setbacks.
Head coach Julian Nagelsmann confirmed on Saturday that the plan remains for Neuer to start the opening group game, with the medical staff satisfied with his progress.
Voller, who serves as sporting director for the Germany national football team, said the goalkeeper has shown clear signs of improvement since joining up with the squad in the United States.
"He has already completed training sessions with the team here in Chicago and shown that his calf is no longer causing major problems," Völler said.
He also highlighted Neuer's vast experience at the top level and his understanding with several teammates, particularly those from Bayern Munich.
"We are talking about Manuel Neuer," Voller added. "He is a world-class goalkeeper who has seen everything in his career. He has more than enough experience."
"He will have a superb tournament, I am convinced of that. We don't need to worry about Manuel at all."