The Hoops, who recorded a first away Barclays Premier League win of the season at Sunderland on Tuesday evening, appear close to appointing Harry Redknapp's successor after chairman Tony Fernandes suggested he has landed his preferred choice
Chris Ramsey has been filling the void on a caretaker basis, with former Tottenham head coach Tim Sherwood the heavy favourite for the position - although Fernandes' comment on Twitter seemed to distance the club from the 46-year-old.
Fernandes said his target was "not what anyone thinks", but admitted the appointment was likely to "take a while".
Laudrup, sacked by Swansea in February, emerged as the new bookmaker's favourite.
However, Laudrup is in charge at Qatari champions Lekhwiya and his representative Bayram Tutumlu indicated there would be several hurdles to overcome before the 50-year-old could be lined up for a move back to England.
"Laudrup is under contract with Qatari club Lekhwiya
Out of respect anyone interested in him should contact the club," Tutumulu said to Sky Sports News HQ.
"I don't think they would let him go because the team are in so many tournaments and competitions."
Ramsey has refused to rule himself out of contention to become the club's new manager on a permanent basis, and has seen his odds shorten after Tuesday's victory, but continues to stress he will do whatever job is asked of him by the board.
QPR are out of the bottom three following the 2-0 win at The Stadium of Light.
Bobby Zamora, who scored the second goal on the stroke of half-time, feels the west London club can now build some momentum, with a trip to fellow relegation-battlers Hull ahead on Saturday.
"It was a massive boost and has been a long time coming, we have been working so hard," he said on the club's official YouTube channel.
"It was a great work ethic
We have had a lot of good performances this season and probably lost a few points which we did not deserve to.
"We will now be looking to keep this going and to get some more points on the board."
Laudrup, who guided Swansea to victory in the 2013 Capital One Cup final, remains keen on a return to the Premier League, but only when the timing is right
Tutumlu added in an interview with the London Evening Standard: " Michael has taken (Lekhwiya) them to first place in the league and he is regarded as the most important person in the club right now
"I don't think it is the right thing for Michael to leave now and go because he has agreed a contract with these people
I don't think it's possible.
"I don't want to speak about whether QPR have been in contact, that's private
I can only say he loves English football and the Premier League
It's just not possible right now
"In June his contract will finish and he will be free
I'm not sure if they will want compensation to let him go now, first QPR have to talk to them
"You can never say never and he could return to the Premier League
If the right club comes, the right project - why not?"
Source : PA
Source: PA