The 22-year-old is seemingly free to join up with the newly-promoted Premier League outfit after QPR agreed a fee with Cardiff City, but the youngster is yet to make a decision.
With Ferdinand reportedly close to joining the Londoners, Redknapp feels that the prospect of playing alongside the veteran will prove tempting for Caulker, whose career could take a similar trajectory as Gary Cahill's.
"Hopefully we can move things along with Caulker and we can have talks later this week," he told The Telegraph.
"The prospect of playing with Rio Ferdinand in the centre of defence is something that will appeal to the lad. He's a young player and he can only improve playing alongside somebody as experienced as Rio.
"If you look at Gary Cahill, he has improved massively playing with John Terry and I believe Rio can do the same for Caulker. That's a deal we would really like to get done."
The former Manchester United and England stalwart will reportedly ink a 12-month contract in West London shortly.