Livermore is regarded highly inside Spurs.
Redknapp said: "I am looking forward to seeing what Livermore can do as I have really been impressed with him in training and his attitude.
"When I came here they were talking about letting him go. They were saying: 'He has had injuries, he is never going to make it.'
"We even had one fella who worked here who said that he couldn't run. I went out onto the training pitch with him, did a running session and I have never seen an athlete like it in my life."