QPR have been strongly linked with the former Tottenham, Portsmouth and West Ham United striker, who is currently playing for MLS side Toronto FC.
Redknapp has made no secret over wanting to sign the striker from Toronto FC, and has worked with him previously at West Ham United, Portsmouth and Tottenham.
The QPR boss told TalkSport: “The chairman will be dealing it. It depends on what the fee is.
“He is now 32. You can’t be playing five, six million pounds for him now and paying him big wages because it doesn’t stack up.
“If the chairman could do a deal, I would love to have him. He would be a great signing for us, but it would depend on the finance of the whole deal.
“Tony Fernandes, Phil Beard and the rest of the people deal with that side and it is up to them to decide if it is a deal they want to do.”
What QPR would get with Defoe is a player with a proven goalscoring record in the Premier League, having scored a total of 185 goals during his time in English football.
It would give them a degree of depth as well, given that Charlie Austin and Eduardo Vargas have found their goalscoring form for QPR recently, whilst Bobby Zamora continues to be a handful for opposition defences.
At 32, Defoe would certainly still have something to offer, and given how closely Redknapp and Defoe have worked together in the past, it could be a productive signing for the club as they look to consolidate their position in the Premier League after they were promoted to the league via the play-offs last season.