Casemiro has said in an interview that Ten Hag has proven he can make United progress, while the midfielder also said he was very happy with his time at the club.
The 31-year-old returned to action in Sunday's 4-2 FA Cup win over Newport County after missing more than three months through injury.
Currently, United sit eighth in the Premier League table but are bottom of the Champions League group stage and eliminated in the League Cup round of 16. The club's only hope of winning trophies this season is the FA Cup.
Ten Hag's position as Manchester United manager has come under scrutiny after a difficult half season and INEOS' purchase of a 25 per cent stake in the club, with Casemiro insisting the Dutchman has proven he can improve the team and make it progress.
Casemiro told CNN: ".Ten Hag proved last season that he can make progress for Manchester United, and the team is now growing and the team is on the rise. Man needs to win and we proved last season that we are capable of achieving great things
Casemiro has not played in the Premier League since the victory over Brentford on 7 October due to ankle and hamstring injuries.
Casemiro joined United from Real Madrid 18 months ago on a four-year contract until June 2026, but according to The Athletic, the Brazilian could weigh his options this month.
Casemiro said: "I really enjoyed my time [at Manchester United] and I try to enjoy it every day. I'm really happy to be back and win with Manchester United, to bring Manchester United back to the top of the table and to help my team-mates. ”
I'm very happy at Manchester United and as I've always said, the fans always help me and the club always treats me well. I'm enjoying the Premier League, I'm enjoying my time at Manchester United and I'm happy to play for Manchester United. ”