The England winger appears to have recovered from a long-standing groin complaint.
"Thursday was probably the best day Aaron has had," said Redknapp prior to Saturday's visit to Sunderland. "He worked hard with the fitness coaches and he is getting there. He is improving day by day and he is not too far away.
"Gary Lewin, the England physio, came down to have a chat with him. They wanted to monitor his progress and see how he is. And he's improving.
"I wouldn't want to be putting a time on when he will be available but he's improving."