Despite offering the Israel International a return to football with a trial at Loftus Road, the 66-year-old, whose side are third in the Championship, has not received a response
The 33-year-old is a free agent after being released by Chelsea at the end of last season, and was offered to the Loftus Road outfit by his representatives.
Redknapp was open to giving Benayoun a trial at the west London club, but explained that he had yet to hear back from the player and any deal looks far from being completed.
“Someone rang me about him a week ago and I said I’d be interested enough to look at him and see how he looks, but I haven’t heard anything more,” Redknapp told The Fulham Chronicle.
“We don’t need anyone but you just never know. We’ve lost Tom Carroll for a few games and things do happen.”
QPR are currently third in the Championship but have failed to win their last two outings, and were beaten 2-0 by league leaders Burnley on Saturday.
Benayoun moved to England in 2005, joining West Ham - once managed by Redknapp - before leaving for Liverpool two years later. More recently, he won the Europa League with Chelsea in his final season at the club.