The Loftus Road side are rooted to the bottom of the Premier League table and Redknapp is desperate to bring in defensive reinforcements, especially with the news that Ryan Nelsen will leave to take the reins at Toronto FC.
Olsson, who has been a key figure in West Brom's strong start to the season, was the subject of a rejected £5m bid from QPR on Thursday and Redknapp is unsure if he will end up in west London this month.
Speaking about Olsson, he said: "We made an offer and it was turned down. I don't know where to go from there. He is a West Brom player. If we could get him it would be great."
Reports on Thursday claimed Palermo were looking to bring Faurlin to Italy but Redknapp says he wants to keep the Argentinian at the club.
He added: "We're not looking to sell (Faurlin). I like him. Smashing boy - he's no problem - and unless I get two or three top midfielders he is very much part of the plans."
Redknapp also admits he is desperate to hang on to Nelsen, despite the defender agreeing to take charge of Major League Soccer side Toronto this week.
Toronto are keen for the 35-year-old to begin work there before 2 March, when the MLS season starts, but Redknapp plans to keep the New Zealander for as long as he can.
"I’m not sure the dates of when Ryan will look to go," said Redknapp. "The longer he is here, the better, because we need him.
"He is a fantastic player, a top professional and we need him for as long as we can. Hopefully we can keep him for a fair bit of the season."