Free agent Benayoun has been without a club since being released by Chelsea at the end of last season.
His representatives recently suggested QPR were among several Championship clubs looking to sign him, leading to reports the 33-year-old was on the verge of a move to the R's.
Benayoun was invited to train with them but Redknapp insists there have been no further developments.
"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 West London Sport.
"We don't need anyone but you just never know. We've lost Tom Carroll for a few games and things do happen."
Benayoun was brought to England by West Ham, where he spent two years before joining Liverpool in a £5million deal.
Three years later another £5m move took him to Chelsea but he made only one Premier League start for the Blues and was loaned out West Ham and Arsenal during his time at Stamford Bridge.