The 65-year-old replaced Mark Hughes in November with the task of trying to keep the struggling club in the top flight.
While there had been suggestions that Redknapp could leave if QPR drop into the Championship, the former Tottenham Hotspur boss has revealed that he is happy to stay put.
"I would want to take it if the chairman wanted me to stay," The Express quotes Redknapp as saying. "I would stay with the club and have a go at the Championship.
"I would do that, but if he said we needed to cut back and I had to go, I would understand that as well. The chairman would have to look at the situation carefully.
"It is well documented that there are a lot of players getting a lot of money here. They would be earning way in excess of what they'd get in the Championship."
QPR are currently seven points from safety.