Greenwood, 21, had been facing charges including attempted rape and assault but the Crown Prosecution Service announced on Thursday the case had been discontinued as "the withdrawal of key witnesses and new material that came to light meant there was no longer a realistic prospect of conviction".
United then issued their own statement which said "the club will now conduct its own process before determining next steps".
Ten Hag was asked about Greenwood at a press conference on Friday but would not go beyond the club statement.
"I can't add nothing," the United boss said. "I refer to the statement of the club. In this moment, I can't give a comment about the process.
"I can't say anything about it, I refer to the statement of the club and at this moment I can't add anything."
Greenwood, who has two and a half years left on his contract, has been suspended from both training and playing for the club since his arrest in January 2022.
Asked if Thursday's news had any impact on his preparations for Saturday's match against Crystal Palace, who held United to a 1-1 draw at Selhurst Park on January 18, Ten Hag added: "We have always to focus on the game, no matter what, it is our job. That is why we are here.
"We have a lot to do against them. Two weeks ago we had a bad performance there, I wasn't happy with the performance from us. It was 90 per cent focus and energy and we dropped two points.
"We have to avoid that tomorrow. We need a better game tomorrow, a better focus in the game, but especially better conduct in the way of play because we have to beat them because that's quite clear."
Ten Hag said Marcel Sabitzer would be in the squad for Saturday's match and could make his debut following his deadline day arrival from Bayern Munich on loan.
Sabitzer has been brought in to provide cover for United's stretched midfield following long-term injuries to Christian Eriksen and Donny van de Beek, with Scott McTominay also sidelined at present.
"He did only one session but you can see he's a very fit player," Ten Hag said of the 28-year-old Austrian.
"I didn't have different expectations coming from Bayern Munich. In Germany their fitness is always good. I think he is ready to play."
United defender Raphael Varane announced his retirement from international football on Thursday after a France career in which he won the World Cup in 2018 and finished as a runner-up last year in Qatar.
France's loss could be United's gain if the 29-year-old is able to extend his club career.
"For United, I think it's good news," Ten Hag said. "Rapha achieved everything in terms of football club wise but also with his nation.
"It is incredible what he achieved, big respect, and I am happy he puts all his energy and experience into the team."