Olsson only signed a new four-year contract with the Baggies in October.
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.
"I can confirm a bid has been turned down and I don't encourage anymore bids because Jonas is not sale," said manager Steve Clarke.
He added: "I have spoken to Jonas and he says he is loving the football here and is looking forward to the rest of the season. He will remain a West Brom player and we don't have to sell anyone. He is not for sale so there is no figure which is reasonable."
But when asked if there is a buy-out clause, Clarke said: "There is a clause in Jonas' contract which comes into play during the summer. There are six clubs that can invoke that."
Olsson is understood to have reservations about any potential move to Loftus Road given their precarious position in the Premier League. In any case, Baggies manager 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.
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, with talks lined-up with manager Redknapp on his future.
- Sports & Recreation