"Joe would be fantastic," Redknapp said. "He's been a good manager, at Hearts and Bristol City, and would be excellent but I really wouldn't want to lose him because for me he is fantastic.
"You'd put your life on Joe. He knows the game, a lovely man and a great character. He's a quiet man but when he says something it's worth listening to. He's a good guy."
Redknapp feels whoever gets the job will have a tough task on their hands.
He added: "It's a hard job whoever takes it. Burley is a good manager but he had a hard job as where have the great Scotland players gone?
"No disrespect to the present squad. They have some decent players, but years gone by they were fantastic. Years ago they were the backbone of every English team. St John, Yates, Law, Baxter and people like that.
"Souness, Hansen. Something happened to Scottish football."