The former England intentional has been a bit part player at Anfield under Brendan Rodgers, leading to speculation that he may leave during the transfer window.
It is thought that the Reds are keen to remove his £90,000-per-week wages from their expenditure as they look to bring in a number of attacking additions.
Redknapp admitted that he is considering in the 31-year-old, but that he will only pursue an affordable deal:
“I have got a lot of time for Joe as a player and a person,” he is quoted The Mirror.
“Joe is interesting for me – 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 (Rogers) when the time is right and see what he has to say.”
Redknapp went on to claim that it may be difficult to attract players to Loftus Road following QPR’s poor start to the season:
“I doubt if we can bring in anyone this week. It is difficult to find players at this time of year.
“Not many players 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.”