Rose has broken into the England U21 team this season and featured in yesterday's FA Cup draw against former club Leeds United.
Redknapp said: "Danny was injured for a long spell when I first came to the club and I loaned him out to Peterborough earlier this year.
"But his attitude has changed, he's worked hard, he's got terrific ability and he can play central or wide left. I also think he could become a top left back one day. He's quick, gets at people, gets his crosses in and I'm looking forward to seeing him play."