Greenwood was arrested on Sunday over the alleged rape and assault of a young woman.
While still in custody, the 20-year-old was further arrested on Tuesday on suspicion of sexual assault and threats to kill.
United started Rangnick's pre-match press conference by saying the German would not take any questions on Greenwood, who was released on bail on Wednesday, while a police investigation was ongoing.
Rangnick insisted United had a "normal" week of training ahead of Friday's FA Cup fourth round match against Middlesbrough despite the Greenwood distractions.
"Obviously, I suppose, it was a topic within the team but they're all human beings and Mason was part of the group until before we had our break," Rangnick said.
"But, as I said, it was a good week of training. We could train under normal circumstances and we are looking forward to the game tomorrow."