The Hoops have been heavily linked with a January move for the England international amid reports the west London side will offer the striker a £90,000-a-week contract.
Defoe is believed to be unhappy at Toronto FC after the Major League Soccer outfit’s owner made disparaging remarks about the former Tottenham star.
While Redknapp revealed QPR did try to sign Defoe in the summer transfer window, the Hoops manager insisted the club have no plans to renew their bid in January.
“We tried to get Jermain before the deadline but at the moment there is no movement on that one,” said Redknapp.
“I’m a big fan, he’s a goal scorer and someone you would want at your club. He’s a player I’m sure we’d be interested in in January. It’s up to the chairman.”
Defoe has scored 11 goals in 15 Major League Soccer appearances after completing a move to Toronto from Tottenham in February.
The ex-West Ham United forward netted 152 goals in 427 Premier League appearances before leaving for the MLS.
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