France international Remy was on the brink of joining Liverpool last month, only for the Merseyside club to pull out of the deal at the last minute.
The striker, who spent last season on loan at Newcastle United, has since returned to training with QPR, but has not featured in their pre-season schedule following his exertions at the World Cup.
However, despite his lack of match sharpness, Redknapp believes Remy may be ready for his side's opening top-flight fixture at home to Hull City next week.
Speaking after QPR's 1-0 friendly reverse to PAOK on Saturday, the former Tottenham boss said: "He's here, he wants to work and get in the team.
"He's worked really hard on the training ground, I couldn't have asked for any more from him. He's trained great and his attitude's been first class.
"Hopefully with a week's training he'll be fit to play next week."
Jordon Mutch made his debut for QPR against PAOK following his move from Cardiff City earlier in the week, and Redknapp was impressed with the 22-year-old.
"It was his first game - he's still settling in, but he'll do well," he added.
"He's got good ability and he's got a good future."
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