Keane, 32, played for Redknapp at Tottenham Hotspur and may be open to a return to the Premier League on a short-term basis, having previously spent time on loan at Aston Villa last season.
"Robbie Keane is a good shout," Redknapp said in Saturday's edition of British newspaper the Daily Telegraph.
"I haven't spoken to him yet but he would be an interesting player. He's a good pro and he'd be an ideal type to have around."
QPR are currently bottom of the Premier League table and without a win in 15 matches ahead of Saturday's home fixture with Wigan Athletic.