Terry will become a free agent on July 1 when he ends a memorable 22-year association with the Premier League champions.
The former England skipper has been linked with a host of Premier League clubs including Stoke, West Brom and Bournemouth while he has also been linked with moves to the United States and China.
But Redknapp is hopeful that he can persuade the 36-year-old to drop down into the Championship and become one of the leading figures at the Midlands club next season.
Terry has already lined up under Redknapp this summer during Michael Carrick’s testimonial at Old Trafford and the Blues boss used the opportunity to have a good discussion with Terry on what Birmingham could offer him next season.
Redknapp, speaking on talkSPORT, said: “I’d love to have him at the football club. He’s a fantastic captain and great leader.
“We’ve made him a good offer and we have done the best we can. It’s up to John now, but we would love him at Birmingham.
“He played for me the other week in Michael Carrick’s testimonial. I had John at the back with Jamie Carragher and I would have them two together all day long. They were fantastic.
“I had a chat with him and said to him come in – he’s doing his coaching badges – have a year or two and who knows what he wants to do in the future?”