The January transfer window is now open and a host of big-name players have already been linked with QPR as Redknapp looks to keep Rangers in the top flight. 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."
He added: "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."
Cole may be of interest to Redknapp but the 65-year-old does not think players are easy to acquire during the transfer window and with QPR in their current predicament.
"It is difficult to find players at this time of year," he said. "Not many clubs let players go and in the situation we are in, they will look to hold you to ransom anyway. They see you are in a desperate situation and try to squeeze the life out of you. It is difficult but we will see. We are looking around.
"I have got a list of names - players I would like to try and get. Actually getting them is not easy. It is all about value, prices and everything else."