Bramble claims he would happily sign an extension at Sunderland if one were put to him, but insists he will not be forcing the issue.
Redknapp is fighting relegation, and QPR are still odds-on for the drop, so would Bramble fancy a drop into the Championship?
London is always a big draw for top players, and that could swing the deal.
Sunderland travel to Loftus Road this weekend.
Titus Bramble: "In football you never know what is going to happen.
"I know I was linked with QPR (in January), but I am not focused on that.
"Sunderland is my team and that is who I am playing for. I will give 100 per cent for Sunderland.
"I didn't know if my time here was coming to an end.
"I didn't think about it. I just came in every day, trained hard and what happens off the pitch will happen.
"I only care about what happens on the pitch.
"What happens in the summer happens. I am happy and settled here.
"I am out of contract. It's up to the manager and the directors what they want to do.
"I will happily sign a new contract here, but it's out of my hands."