Both players are out of contract this summer at Manchester United and Chelsea respectively and have been linked with moves to QPR, who achieved instant promotion back to the top flight by winning the Championship playoff final on Saturday.
Despite being in the Premier League again, Redknapp doesn't think that he will be able to tempt the duo, who he managed at West Ham in the early stages of their careers, to Loftus Road.
Speaking at the launch of QPR's new kit earlier today, Redknapp told Sky Sports News: "I would think there's absolutely no chance of getting Frank. He's at Chelsea.
"I'd be very surprised if Chelsea don't keep him anyway - he's just been such a fantastic player.
"Rio's now a free agent but I'm sure he's going to have so many offers. Again, I love Rio, I signed them both as 15-year-olds but the chances of getting them to QPR are very slim."
Redknapp also admitted that it would be difficult to keep French striker Loic Remy at the club despite their promotion.