Sabitzer joined the Red Devils from Bayern Munich in the January transfer window on a contract that runs until the end of the season.
United's agreement with the Bavarians does not include the option to make the move permanent at the end of the season.
Sabitzer has made 13 appearances for Erik Ten Hag's side so far and has scored three goals, including a brace in a 2-2 draw against Sevilla in the Europa League on Thursday.
The 29-year-old Austria international played his part as United beat Newcastle United to win the Carabao Cup in February.
Sabitzer has enjoyed his short spell at Old Trafford and wants the adventure to continue.
"I didn't have to think for 10 seconds after United called," Sabitzer said in an interview with German publication Bild. "I said straight away, if the time works, we'll do it!
"This is initially a project until the summer, then we'll see. Until then, I want to give everything here. It's a loan deal with no options. The situation will be assessed in the summer.
"But I can say for myself, I have found my place here. I know the Premier League now and I can say there is nothing better, more intense or tougher.
"Every game is a fight, everything goes faster. This is the best league in the world. Once you have played here, you know it's incomparable.
"Of course my thoughts on United – especially looking at how things are going and the confidence I get from Erik ten Hag – are very positive. But I don't have to decide it alone."
