Newly-promoted QPR have agreed a fee with Cardiff for Caulker, who has also been linked with a move to Crystal Palace.
Cardiff boss Ole Gunnar Solskjaer is waiting for the 22-year-old England international to make a decision and Redknapp is hoping that Caulker will opt for a transfer to Loftus Road.
Redknapp is also close to finalising the signing of Ferdinand and believes the chance to play alongside the ex-England captain will appeal to Caulker.
"Hopefully we can move things along with Caulker and we can have talks later this week," the QPR manager told the Daily 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."
Meanwhile, Redknapp is looking forward to the prospect of adding Ferdinand to his squad, with the centre-half expected to sign a one-year contract at QPR following his departure from Manchester United.
He added: "Rio has always been a class act and signing a player like him will give the whole place a lift.
"He's never been a greedy lad and this deal is not about money. He's still desperate to play in the Premier League and it will help that we’ve worked together in the past."