Beckford took his tally to the season to 24 with a brace against League One promotion rivals Colchester last weekend.
The frontman may have withdrawn his transfer request but, given Beckford is out of contract at the end of the season, Redknapp would not be surprised to see a club make their move in the summer - with Championship leaders Newcastle a likely interested party.
"He did well and would be a good gamble for someone in the Premier League, I am sure someone will take him," said the Spurs boss ahead of Wednesday night's trip to Elland Road.
"He is a free at the end of the season, and someone has probably done a deal with him, rather than paying a couple of million for him now.
"They will wait and take him at the end of the season on a free."
With Robbie Keane having joined Celtic on loan, Redknapp confirmed centre-back Michael Dawson would step in as skipper again, given Ledley King will be rested.
"Michael Dawson has been captaining the team, and has done a good job," the Spurs boss said.
"He signed a new contract, has been in great form, a real leader who leads by example and so he will be captain the team against Leeds."
Striker Roman Pavlyuchenko (groin) is not expected to feature on Wednesday night, while new signing Eidur Gudjohnsen is unavailable as he was not involved in the original tie.
With fellow new recruit Younes Kaboul and Kyle Walker, recalled from Sheffield United, both cup tied, Redknapp admits the deadline-day deals have left his options somewhat limited.
"We are one or two down in terms of numbers, but it will be an opportunity for a couple of youngsters to come and sit on the bench," he said.
"I will speak to (academy manager) John McDermott and (under-18s coach) Alex Inglethorpe to see which players deserve that opportunity."
Redknapp added: "It will be a tough game. They will be difficult opposition and played ever so well at White Hart Lane, even though we should have won the game.
"They are a team who can play way above their level, but we are doing well, with just two defeats in 12 games."
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