Back in May, Mr Trump told Good Morning Britain: "He works for me. I mean, he's doing a nice job but don't forget, he works for me – I make money from The Apprentice.
"When we first chose him for the show, he was so low on the economic scale, he didn't really fit the role. I think he's made more money by being on The Apprentice than he has in business.”
The Apprentice returns next week on BBC
During the show's press conference which HELLO! Online attended, Lord Sugar fired back, saying: "Yeah, he also said he's gonna build a wall. I was telling my American friends, I'm wondering why he hasn't also claimed that he's going to stop all snow storms in future in New York.
"I do think it doesn't warrant any response to that nonsense. It's complete and utter nonsense, and he's got nothing to do with this programme, other than he was once the host of the American show, and left under a cloud of uncertainty with NBC."
Lord Sugar added: "He's not as good as me as far as The Apprentice is concerned. He's not in my class quite frankly."
"He's not as good as me as far as The Apprentice is concerned," said Lord Sugar
Mr Trump left his role on the American version of the show last year to concentrate on his current US Presidential run. The politician and his rival Hillary Clinton clashed in a televised debate on Monday.
"I've seen clips of their debate and what comes to mind is that it's a US version of Would I Lie to You?" joked Lord Sugar. "All that was missing was Rob Brydon in the middle."
On a more serious note he added: "As many people have said, it is quite a frightening thought that he may be the most powerful man in the world shortly."
Karren Brady, who returns as one of Lord Sugar's aides alongside Claude Littner, added: "For me personally I think Hillary Clinton, another woman leader in the world, means that the world is a safer and better place."