The striker has played under Redknapp at three different clubs - West Ham, Portsmouth and Spurs - purchasing the England international at all three and most recently parting with a reported £15 million to take him back to White Hart Lane in 2009.
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"I'd love to have Jermain," Redknapp is quoted as saying in the Evening Standard.
"We made an enquiry but at the moment he’s not available. We’re nowhere near anything. There is a small chance of it happening."
QPR have recently allowed Loic Remy to join Newcastle on a season-long loan, and recruited frontman Charlie Austin from Burnley, but missed out to Norwich for the signature of former Celtic star Gary Hooper.
Tottenham, meanwhile, strengthened their forward line this week with the signing of Roberto Soldado from Valencia for a club-record £25.9m fee.