The Hoops had a reported £5m bid for the Swedish defender turned down by the Baggies on Thursday, despite Olsson supposedly being keen to move to London for personal reasons.
With New Zealand international Ryan Nelsen set to depart Loftus Road to take over the managerial position at Major League Soccer’s Toronto adding to QPR’s defensive woes, Redknapp is keen to strengthen his back four.
But the Hoops boss is pessimistic about the prospect of luring Olsson to west London.
“We made an offer for Jonas Olsson but as far as I know, it’s been turned down,” he said. “I don’t where we’ll go with that one. He belongs to West Brom.
“Obviously we made an offer because we like him. If we could get him that would be great, whether it goes anywhere, I don’t know.”
Another defender linked with a switch to the struggling west London outfit is Gallas, who Redknapp worked with during his Tottenham reign.
But with the France international still very much in contention for a first-team place at White Hart Lane, the R’s boss doubts the centre-half would be interested in moving to Loftus Road.
He continued: “William is a good player. But he’s well in at Tottenham and is playing regularly, so I don’t see him going.”
Redknapp’s QPR headache is not exclusive to his defenders. Their inability to score goals also a serious concern, with the Hoops managing a distinctly average 17 this term.
Djibril Cissé has struggled to match his exploits in the second half of last season, while for all Jamie Mackie’s effort, the Scot is not a prolific goal-scorer.
With Andy Johnson and Bobby Zamora both still injured, Swansea’s out-of-favour Graham is being touted as an option for Redknapp, but the QPR boss does not expect Michael Laudrup to allow the striker to leave.
“He belongs to Swansea but he’s a good player,” Redknapp added. “At the moment he’s playing for Swansea and going well for them. I imagine they wouldn’t want to sell him.”