The 25-year-old Austin, whose 11 goals so far this season make him the league's top English scorer, has 18 months to run on his contract.
"He’s not going anywhere in January. He’s here and it’s up to Charlie and everyone else. I’m sure we want to keep him long term," Redknapp told reporters ahead of Friday's Arsenal trip.
"But it’s like everything, we’ve got to stay in the division this year, which I’m confident we will do, and Charlie’s proved that he’s a Premier League player.
"He wants to play in the Premier League for the rest of his career if he can. He’s got to keep scoring goals, that’s all he’s got to do."
Rangers have yet to earn a point away this term but 17 home points have lifted them out of the drop zone into 16th place.
They will be without South Korean left-back Yun Suk-Young, a stalwart this season who has been ruled out until the New Year with an ankle injury, for the match at sixth-placed Arsenal.
Redknapp has said QPR are more likely to seek loan deals in the window than to buy players, despite former England striker Jermain Defoe reportedly being eager to link up again with the ex-West Ham United, Portsmouth and Tottenham Hotspur manager.
"We’re not looking to spend money in the window, we’re looking to get a couple of loans in if we can, good loans, and that’s where we’re at," said Redknapp.
"We bought some players in the summer, so now we’ve got a good squad we’re looking to bring a couple of loans in - we’re not looking to be spending big money in the transfer window."
(Reporting by Alan Baldwin, editing by Ken Ferris)
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