Redknapp had been hoping to persuade the former West Ham player to move to Tottenham Hotspur however a deal to take Cole to Old Trafford may have already been completed.
“I’ve got a feeling that it might have been done (for Cole to join United),” he said.
“It wouldn’t surprise me in the least. Joe’s not wanted to speak to anybody and his people have been saying ‘let’s get the World Cup out of the way first’.
“But we’d be interested for sure. I like Joe.”