Redknapp worked with the 30-year-old at Portsmouth and West Ham United.
He confirmed that the deal is a long way off, though there is still a small chance of it happening.
"I'd love to have Jermain," Redknapp told the Evening Standard.
"We made an enquiry but at the moment he's not available.
"We're nowhere near anything. There's a small chance of it happening."
Defoe may have to settle for a second-choice role after Spurs broke their transfer record to sign Spain forward Roberto Soldado, while QPR are keen to add to their front line after Loic Remy joined Newcastle United on a season-long loan.