The star was speaking to US shock jock Howard Stern on the radio when he was quizzed about his love life.
When asked if he was engaged, the 51-year-old TV guru reportedly said he was "not sure".
The DJ asked him: "Why is the question 'are you engaged?' so painful to you?"
He said to the music mogul: "You seem embarrassed by the women you date, and I'll tell you why, they are lovely women, but yet you won't talk about about them.
"I'm a married man ... and if someone asks me a question about her I am proud to answer them, proud to admit I have a relationship with her."
Cowell replied: "If we were having this conversation off the radio I could have a normal conversation with you."
Cowell and make-up artist Hussainy have been together for almost two years.
According to reports, Simon told the show that he still loved his ex Terri Seymour, revealed that he had once had a threesome, and said he had a "bizarre kind of blind date" with a heavily pregnant Denise Richards.
A spokeswoman for Cowell told The Sun: "Simon was just making it clear that he doesn't discuss his relationships."