"I have to say that I would have picked him," Redknapp said.
"David has been a fantastic servant to all his clubs and a tremendous ambassador for football.
"He trained with Tottenham in January 2011 and we looked at signing him on loan when the American season ended. Putting him in the Olympics squad would not have hurt.
"Fair play to Stuart (Pearce). He's always been his own man, which is what you have to be if you want to make it as a top manager. It's up to him to select the best squad at his disposal, that's what he believes he'll do."