The 66-year-old was placed in interim charge of the R's after Chris Ramsey was sacked on 4 November.
He oversaw the 0-0 draw with Preston on 7 November and has brought in Kevin Blackwell to assist him at Loftus Road.
Warnock, who was boss of QPR from March 2010 to January 2012, returned to the Championship club in an advisory role in October.
QPR's next two matches are at Middlesbrough on Friday and home to Leeds next Saturday, suggesting an appointment before their trip to Reading on Thursday, 3 December.
Former Leicester boss Nigel Pearson has been linked with a move to west London, while Burton Albion say they have not received an approach from the R's to speak to manager Jimmy Floyd Hasselbaink.
Under Warnock's leadership, QPR were promoted to the Premier League in 2011 as winners of the Championship, but he was sacked the following January with the club 17th in the top flight.
He had been out of management since being dismissed by Crystal Palace in December 2014, after four months in charge.
After joining QPR in an advisory capacity to Ramsey in October, Warnock said "full-time management doesn't interest me any more".
Rangers are 13th in the Championship table, eight points off the play-off places.

Kuba Oles was travelling at a minimum of 80mph (129km/h) when he hit Georgie Ann Evans' car in Dudley on 27 October.
Oles, 25, who had sped down Priory Road, only suffered minor leg injuries, West Midlands Police said.
Oles, from Beaconview Road, West Bromwich, admitted causing death by dangerous driving when he appeared at Wolverhampton Crown Court.
He was also disqualified from driving for 14 years.
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PC Alan Wood, who headed the police investigation, said: "His driving on this day was extraordinarily dangerous and inevitably put other road users in peril.
"During police interviews he attempted to blame Georgie for being an [inexperienced] driver and pulling out too slowly.
"That was proved in court to be completely false and Oles was described as a dangerous person who posed a significant risk of causing the public harm."
Oles was also sentenced to nine months in prison, to run concurrently, for another dangerous driving offence which he also admitted.
Ms Evans's family said in a statement: "We give our thanks to the justice system for handing down the sentence they were able to.
"Unfortunately we are paying the ultimate sentence - the loss of our daughter."
Neil Warnock expects to be in charge of Queens Park Rangers for two more games, BBC Radio London reports.
[NEXT_CONCEPT]
A man who killed an 18-year-old motorist in a crash that split her car in two has been jailed for six years.