Lord Sugar's name was in the pipeline when host Donald Trump quit to run for political office.
The US show, called Celebrity Apprentice, features famous celebrities working in teams to win challenges. The goal is to raise as much money as possible for charity.
Speaking at The Apprentice press launch, Lord Sugar said: ''They did consider me but to be perfectly blunt, the American public don't know who I am, which is fine, that's why I spend most of my time there.
"It would have been an interesting thing to do but the producers decided they needed someone who the American public knew.''
It was revealed in September that Hollywood action film star and former California governor, Arnold Schwarzenegger, would be taking over the role from Donald Trump.
Lord Sugar joked: "They've got Arnie now - I can't wait to see what a cock-up he's going to make of it!"
The new series of The Apprentice returns to BBC One on Wednesday 14 October at 9pm, with a second episode airing the following evening on Thursday 15 October.
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