The Israeli, who has been a free agent since his release by Chelsea at the end of last season, has recently been linked with a switch to Loftus Road.
Redknapp has confessed that he would be willing to hand the 33-year-old a trial, but is unsure if he would be prepared to offer him a permanent contract.
"Someone rang me about a week ago about him and I said I would be interested in having a look at him, but never heard no more," Redknapp told the Fulham Chronicle. "He's very similar to what we've got here. If you get injuries, you never know, do you?"
As well as Chelsea, Benayoun has also turned out for West Ham United, Liverpool and Arsenal in the Premier League.