The 38-year-old only moved to Ibrox in July and has impressed in 14 outings so far.
However, he is yet to be offered a new contract by Rangers, despite his current deal expiring at the end of the campaign, and QPR could approach him next month ahead of a possible summer return.
The Daily Record reports that interest from new R's manager Ian Holloway could prompt Rangers into action, with their boss Mark Warburton keen to keep Hill around next season.
And it is claimed that an Ibrox extension would be the Liverpudlian's preferred option.
Hill was released by Holloway's predecessor Jimmy Floyd Hasselbaink at the end of last season, after 185 appearances and two promotions at Loftus Road.
Glasgow Rangers are also keen to extend the contract of veteran striker Kenny Miller.
The 36-year-old has been involved in eight goals in 17 Scottish Premiership appearances this season, scoring four and making as many.