Cudicini has been given a free transfer from Chelsea and could make his debut against Stoke on Tuesday as first-choice goalkeeper Heurelho Gomes has a thigh strain.
Chimbonda was not registered in time to face Tony Pulis' men in the Premier League clash at White Hart Lane, but he will be available at the weekend after following Jermain Defoe as the second player to rejoin Spurs this month.
Another who left Spurs in the last year was Keane, who has struggled to make an impact at Anfield and was not in the squad for the FA Cup clash against Everton at the weekend.
"I wouldn't sit here and say I wouldn't like to have Robbie Keane at my football club, I'd be a liar, but he belongs to Liverpool so it is not an option unfortunately," Redknapp said. "As a player and a person I have a lot of time for Robbie Keane. I think he's fantastic."
Keane's omission fuelled concerns about his future, although Liverpool boss Rafael Benitez has previously stated there will be no departures in the current transfer window.
