Redknapp said: "I worked with him last year and it wasn't a complete surprise he was named manager. The big surprise was Jose Mourinho had left the club, it was amazing to me. Obviously he had done a fantastic job at Chelsea over the last few years and that was the massive surprise.
"They've got a game on Sunday and someone is going to have to take charge. Avram is there, he is experienced, he knows the game, he is a clever guy and I just felt I could see him stepping in there, but in the long term I'm not sure.
"What a job for Avram to have, it's a fantastic opportunity for him. He is now managing one of the top football clubs, with one of the best teams in the world.
"It's a great chance for him. Somebody has to take the job and I would love to see Avram do well. I'd love to see him go in there and make a big success of it because he's a smashing guy."