Redknapp admits a move for free agent Keane, 36, could potentially happen later in the window.
He said of the former Liverpool and Tottenham striker: “Robbie is a player you would love to have around your football club.
“He is just a fantastic professional footballer, a great trainer, enthusiastic person, an absolutely buzzy character.
“We haven’t spoken to Robbie but I wouldn’t want to be a liar and say I’m not interested in him and then two weeks later bring him in.
“Any football club with Robbie Keane in is a better football club.
“He can bring an awful lot to any club. At the moment I haven’t done anything but it’s not an impossibility.”