"I see it being repeated everywhere," Clifford says. "But when I asked him last Wednesday, when he and Mezhgan were about to fly back to L.A., I said, 'Are you engaged?' His answer was, 'Max, I'm not engaged.' That was last Wednesday."
Clifford adds that he spoke to Cowell's mother over the weekend, and she also denied that Simon was engaged.
But Clifford, who is getting married himself in a few weeks, says he wouldn't be surprised if Cowell followed him down the aisle sooner rather than later.
"I said to him, 'So, there's going to be two weddings this year?' " Clifford says. "Normally he would say, 'Don't be so ridiculous' or 'In your wildest dreams.' But he said, 'Who knows?' "
Whatever their official status, Clifford says that Cowell, 50, and Hussainy, 36, make a great couple.
"They have known each other for years," he says. "They've actually been going out together for the last year. She knows him, she's been around him. So, she knows the person he is, and he knows the person she is. That's why it works so well."
He adds: "They are very suited. She is someone who is independent and says what she thinks and feels, and he likes that. He's probably the happiest I have ever known him in the nine years I've been working with him."