The 65-year-old has readily acknowledged the Hoops must strengthen with the west London outfit languishing in 20th position in the Premier League table.
Cole has scored just once but the former Chelsea star is yet to start in the English top flight this season, making six appearances from the bench.
Redknapp previously worked with Cole at West Ham United, and the Hoops boss is keen to bring the England international to Loftus Road to aid their chances of beating relegation.
“I’ve got a lot of time for Joe, as a player and a person, he’s a good lad to have around your football club, a good player,” said Redknapp.
“He’s interesting me. I’d like to bring him here if we could. We’ll see what happens.”
Redknapp also conceded QPR would not be able to afford Cole’s current wages, and should a deal materialise, there would need to be a compromise struck among all parties.
“The deal would have to be right for the club,” Redknapp added.
“We couldn’t do a deal with Liverpool with what his contract is at Liverpool. We’d have to try to find a way of doing a deal with Liverpool, if they’re willing to let him go.
“I’ll have to speak with Brendan, I’ll have a chat with him when the time’s right and see what he has to say.”
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