Ramsay has left Ten Hag's staff to take charge of Minnesota United.
"So it is not a good time in the season," Ten Hag told manutd.com. "But we won't stop him.
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"He is a very good coach, he developed and we are very proud, as Manchester United, that we develop, not only players, but also coaches. And he has a great opportunity. He has to take this.
"We wish him all the best.
"I am sure he will be a great manager in the future," predicted the boss. "He has fantastic skills.
"We will miss him - as coach and as a person. But, as I say, we wish all the best for the future and we look forward to (seeing) the results of Minnesota and we will look forward to how he will be progressing there."