The Sweden international is reported to be keen on a move to London for family reasons, but Albion have turned down the offer from Rangers.
Olsson is also understood to have reservations about any potential move to Loftus Road given their precarious position in the Barclays Premier League.
In any case, Baggies manager Steve Clarke made it clear last week he has no desire to let Olsson go during the January transfer window - and that stance has not altered.
Clarke said: "Why would I expect to lose Jonas in January? January is the silly season.
"We can hang on to every single player. We don't have to sell anybody."
Olsson has also been linked with Arsenal, amidst speculation he has a get-out clause in the contract he signed three months ago.
The 29-year-old has been one of Albion's key performers since joining them four-and-a-half years ago. His form for the Baggies has also led to him becoming a regular for his country.
The bid for Olsson comes as no surprise as QPR manager Harry Redknapp has made no secret of his desire to strengthen his defence during the January transfer window.
That need has been heightened by the fact Ryan Nelsen this week agreed to become head coach of Major League Soccer side Toronto FC.
The 35-year-old has been one of the Hoops' best players this season, but admits he is "playing on glass knees and glass ankles" and is hoping to negotiate an early exit from Loftus Road.
Nelsen has now returned from Canada and trained with the west Londoners on Thursday, with talks lined up with manager Redknapp on his future.
But despite the need for reinforcements, Press Association Sport understands that the QPR boss is not after Tottenham centre-back William Gallas, contrary to reports.
Meanwhile, Robert Green has distanced himself from links to Nottingham Forest. The QPR goalkeeper has lost his starting berth to fellow summer signing Julio Cesar but told talkSPORT: "This is the first I've heard about Nottingham Forest. I don't know anything about it."