The Rs manager has admitted he is interested in signing the Liverpool midfielder and says he will talk to Brendan Rodgers as he attempts as his wages may prove a stumbling block
The Hoops begin 2013 bottom of the Premier League and linked with a whole host of players and Redknapp has admitted Cole is a transfer target.
"I’ve got a lot of time for Joe as a player and as a person,” said Redknapp.
“I’d like to bring Joe here if I can but the deal would have to be right for the club.
“We couldn’t do a deal as it [Cole's wages] is at Liverpool. I’ll have to speak to Brendan Rodgers. We’ll have a chat when the time’s right.”
The former Tottenham boss has also been reported to be interested in signing Nicolas Anelka and Loic Remy but Redknapp says he is not expecting any deals to be done early in the window.
"I wouldn't have thought so," Redknapp told Sky Sports when asked whether there would be any new arrivals on New Year's Day.
"We're not doing anything really, we'll just wait and see. We've got a game tomorrow against Chelsea, then a cup game [against West Brom] and we've got a little break after that, so we'll see what happens.
"It's difficult at this time of year, it's very difficult to make signings.
"Who's going to let people go? People hold you to ransom if they know you're desperate. It's a very difficult time."