Redknapp is hopeful of persuading Defoe to spearhead his new-look attack in the Championship, with the promise of first-team football and a starring role in West London.
The Hoops are lining up a £6m bid for the 30-year-old, but face competition from Stoke City, according to The Mirror.
Redknapp teased QPR fans yesterday with the promise that he is chasing marquee signings before the transfer window closes.
He told reporters: "I am going to put together a team that will excite people.
"I am trying to bring players in who will blow people's minds. I have got the backing of the board to do that, and we are moving on from last season."
Defoe, who has two years left on his contract at White Hart Lane, scored 15 goals in all competitions last season in a campaign hampered by injury.