The 32-year-old midfielder has slipped down the pecking order at White Hart Lane following the summer arrivals of Paulinho and Nacer Chadli.
Former Spurs boss Redknapp hopes he can tempt Parker to Loftus Road and throw him into a Championship promotion push.
Reports have claimed that the England international underwent a medical at QPR on Tuesday and that a deal is close to being completed.
There remains a chance that a late bid from a rival could leave Redknapp empty-handed, with Fulham and Crystal Palace among those reported to be plotting a raid for Parker, but the R's are confident they will get their man.
Redknapp is quoted in the Daily Telegraph as saying: "We're hopeful of getting Scotty signed soon. He's a great lad and will be a really good signing for us.
"He's a player that can do a job for us in the Championship and it's important to have someone like him around the dressing room."