Redknapp confident of Defoe's January arrival
The 31-year-old moved from Tottenham to Toronto in February and has been a hit in the MLS, scoring 11 goals in 16 appearances.
Redknapp was keen to bring Defoe back to England but was unable to conclude a deal before the transfer window shut on Monday.
But he is confident on the England forward - who he has previously worked with at West Ham, Tottenham and Portsmouth - arriving at Loftus Road in January as QPR look to avoid relegation.
"There is every chance he will come in January," Redknapp told talkSPORT.
"I'm a big fan of Jermain's. Almost certainly, I think we will [go back in for him].
"I've signed him so many times. I've taken him everywhere."
Redknapp revealed that Defoe did want to come to QPR but added that Toronto were not willing to let the player go during the MLS season.
"We tried all day with Jermain Defoe," he added.
"He was keen to come. We agreed a deal with Toronto but they wouldn't release him now.
"We could do a deal and then take him in January but we wanted to get someone in today."
QPR had to settle for the deadline-day arrivals of Sandro and Niko Kranjcar, who joined from Tottenham and Dynamo Kiev respectively.
Sandro's deal is permanent while Kranjcar has joined on a season-long loan, linking up with Redknapp for a fourth time.
QPR lost their first two Premier League matches but hit back with a 1-0 triumph over Sunderland on Saturday.