The 25-year-old has made just two appearances for the Red Devils this season, with Diogo Dalot being the preferred right-back choice.
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Wan-Bissaka has struggled at United since his move from Crystal Palace in 2019, and his current season has been affected by injury.
He has recently been linked with a move away from Old Trafford, but Ten Hag played this down.
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"It's clear, he has a future," he said after the 2-0 Carabao Cup win against Burnley in which he played.
"He had some good years here at Man United, but from the start this season he had a lot of illnesses and injuries.
"From the restart on, he's fit, he could train with the team, and you see him progressing. His fitness level is getting better, his performance level is getting better and I'm really happy with his performance [against Burnley].
"If you then give an assist, especially the way he gave an assist, his movement in the right moment, the timing, great pass of course from Bruno, but the assist is great… So I'm happy with his performance, he did good."
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talkSPORT understands that Wan-Bissaka's former club Palace want to re-sign the right-back in the January transfer window.
Fellow Premier League side Wolves are also interested, but United would need to first find his replacement before considering a departure.
Wan-Bissaka's first start of the season came in their victory against Burnley on Wednesday night, and he played 72 minutes of the game.
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He assisted Christian Eriksen for their first of the night, before Marcus Rashford netted a superb second.
The defender had played just four minutes during the campaign before then, coming on as a substitute in their win against Liverpool.
Although he has featured very little for United, it's apparent that he may still have a future at the club with Ten Hag.