Sabitzer joined the Red Devils on loan until the end of the current campaign, having sealed a switch to Old Trafford on transfer deadline day last month.
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The Austria international was drafted in by United boss Erik ten Hag following the injury to Christian Eriksen.
He has made four appearances so far for United, following Eriksen's injury, Casemiro's now-served suspension and Scott McTominay's previous unavailability.
The 28-year-old found game time limited at Bayern and has relished the opportunity to play more frequently.
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His agent, Roger Wittmann, believes Premier League football is suited to his client, and he suggested he could make his move permanent in the summer.
"At Manchester United we see Marcel from Leipzig again. I'm very happy for him," Wittmann told SPORT1.
Asked what happens in the summer, he replied: "We'll see when the time comes."
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SPORT1 also claims the Bavarian giants would also be open to the idea of a permanent transfer.
The Bundesliga champions would like to at least recoup the £13.2million [€15m] they paid RB Leipzig to secure his services in August 2021.
Sabitzer is under contract with Bayern until June 2025, and his box-to-box style fits English top flight football, according to Wittmann.
"Marcel is a top player. It doesn't surprise me at all that he's performing so well so quickly," he said.
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"If you have as much experience as Marcel, whether in the Champions League or with his more than 60 international matches, it doesn't take long to find your way around a club and a league like this.
"He loves this English hardness! It was clear from the start that the Premier League was a great fit for him. He's an aggressive player. He does exactly what he can there. And that's what's needed there."