Redknapp takes his side to west London rivals Chelsea still marooned at the foot of the Barclays Premier League after taking over at Loftus Road in November.
The January transfer window is now open and although the former Tottenham manager was not forthcoming with specific targets he was full of praise for Cole, a player who he managed as a youngster at West Ham.
"I have got a lot of time for Joe as a player and a person," he said. "He is a good lad to have around your football club - a good player.
"I would like to bring Joe here if we could but the deal has to be right for the club.
"We couldn't do a deal for what his contract is at Liverpool. We would have to look at doing a deal with Liverpool if they are willing to let him go.
"I will have to speak to Brendan (Rodgers) when the time is right and see what he has to say."
Redknapp knows his side face a tough task to leave Stamford Bridge with a result on Wednesday and was full of praise for Rafael Benitez.
"Rafa has gone in there, they have got fantastic players and he will do a good job there," he said.
"He will do an excellent job there - he is a top manager. His record is top class. But he has taken over an outstanding group of players - they won the Champions League last year."