The 32-year-old Defoe, who scored 124 goals during his time in the Premier League, has previously worked under Redknapp at Tottenham Hotspur and Portsmouth.
The QPR coach came close to signing the former England international again from Major League Soccer (MLS) team Toronto during the summer but a deal did not materialise.
British media claimed on Tuesday that a deal had been done to sign the striker in January but Redknapp said nothing had been confirmed, though he would continue to pursue the player.
“No, I don’t think anything is anywhere near being concluded with Jermain,” Redknapp told a news conference on Thursday.
“We tried to get Jermain before the deadline (in the summer transfer window), but I don’t think there is any movement on that one at the moment.
“I am a fan of Jermain’s, I have signed him enough times. He is a goalscorer and obviously a player you would like at your club, if possible, but the figures would have to be right.
“He is a player I am sure we would be interested in, in January. It depends on the expense of it all and what the deal is. Tony (Fernandes, QPR chairman) would deal with that, so it’s up to him,” he added.
Since Defoe moved to Toronto from Tottenham in February this year he has been overlooked for Roy Hodgson’s England squads and only made the standby list for the 2014 World Cup.
A return to England could be mutually beneficial for the player and the club, giving Defoe renewed hope for his international career while adding firepower to a QPR squad that is second from bottom in the league table after 10 games.
Redknapp’s side host champions Manchester City in the league on Saturday.
(Editing By Martyn Herman)