However, United have been hit with a double injury blow as Brazil midfielder Casemiro and Argentina defender Lisandro Martinez are likely to be sidelined until late December.
"Casemiro and Martinez are really strong injuries, I don't expect them back before Christmas," Ten Hag told a news conference on Tuesday.
Casemiro picked up a hamstring injury in the League Cup fourth-round loss at home to Newcastle United last week, while Martinez has had a second operation on a recurring foot problem he first suffered against Sevilla in April.
Rashford, who suffered a knock in training before the Premier League clash, was criticised by Ten Hag for attending his birthday party celebrations hours after last month's 3-0 home defeat by Manchester City, calling it "unacceptable".
"Rashy missed a game because of a small knock. He is 100 per cent (ready). Marcus is very committed to Manchester United. He is putting in a lot of work in training to get back to fitness," Ten Hag said of the England international.
Despite intense criticism over his side's performances, the Dutchman was confident they would continue to improve.
"The only thing for us is (to get) three points (at Copenhagen). We have to put ourselves in a position to go through (to the last 16)," he said.
United are third in Group A with three points above the Danish champions who have one point. Bayern Munich lead the table with nine points ahead of Galatasaray on four.
Ten Hag believes United can get back to winning ways but they need a settled team to produce their best football.
"Getting more to our best eleven and getting routines into the team," he said. "So far, we have had to change a lot of things. The balance in midfield is not there. I am sure that when we have it, we will play better.
