Gunners manager Arsene Wenger was believed to be considering a move for the former West Ham man for much of the summer, following the sales of Cesc Fabregas and Samir Nasri. However, Redknapp was able to secure the England international's services before he had a chance.
"I thought maybe [Arsenal] would take Scotty. That was always my one concern," he said. "We wanted him and Arsenal were always the team and then Chelsea came in for him and I thought maybe he might go there. But I thought Arsenal might take him.
"They nearly took [Gary] Cahill from Bolton. I thought they wanted to take Scott. I could see him going there.
"I think in the end we went in for Scott when there was no-one else there, really. He is not going to move up north to wherever. I think Tottenham was the move he really wanted."
The former Newcastle and Chelsea midfielder sealed the move to White Hart Lane earlier this summer, after handing in a transfer request at Upton Park.