Ahead of the thirteenth series launching next week, Lord Sugar said he wants to see a 'Where are they now?' spin off.
While there are no plans to air such a show just yet, Lord Sugar said of the past Apprentice champions: "They've turned into great business people."
"I think the BBC need to do something about that. They need to do a programme, for example, on where they are now," he said.
"They're all doing very well," Lord Sugar explained. "They don't get enough publicity. The BBC doesn't get enough publicity over the real purpose of this programme and one of the real reasons I do this.
"I enjoy watching these young people grow a business from scratch which is what I did nearly fifty years ago.
"I get a great buzz from it."
Suggesting that the spin-off would help inspire young entrepreneurs, Lord Sugar continued: "Some of these people, their lives have changed.
"They've bought houses, most of them have got married, they've got families, they've got security and they're employing people and they've turned into great business people.
"That's what motivates me to carry on doing it and I think the BBC need to do something about that."
However he claimed that strict BBC rules made such a show unlikely.
“There’s a problem the BBC have with compliance, something to do with promoting businesses to do with me, so they can’t do it," he added.
It was Alana Spencer who won The Apprentice last year in 2016, securing a £250,000 investment from Lord Sugar into her bakery business.
The Apprentice 2017 begins next Wednesday night at 9PM on BBC One.