Crystal Palace are regarded as favourites for the England international.
But the Telegraph says Redknapp is finalising a deal for Rio Ferdinand and believes the former England captain's arrival could prove pivotal in his £8 million bid for Caulker.
"Hopefully we can move things along with Caulker and we can have talks later this week," he said.
"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."
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