The couple, which celebrated its second wedding anniversary on Monday (14Sep15), has been open about its dreams of having a big family in recent years.
Teigen previously said, "We want a lot of kids. I would love to have three or four of my own, and then adopt a few. So basically I'll be pregnant the rest of my life."
However, the Sports Illustrated beauty admits she has since tired of answering intrusive questions about when the stars will have their first child - because she has been secretly struggling to fall pregnant for quite some time.
Opening up about her fertility fight during a taping of her new U.S. talk show FABLife on Wednesday (16Sep15), the 29 year old said, "I will say, honestly, John and I are having trouble. We would have kids five, six years ago if it'd happened. But my gosh, it's been a process!"
She added, "So, anytime somebody asks me if I'm going to have kids, I'm like, 'One day, you're going to ask that to the wrong girl who's really struggling, and it's going to be really hurtful to them. And I hate that. So, I hate it. Stop asking me!'"
Teigen's confession was made on the same day her co-host Tyra Banks revealed she, too, had been trying desperately to have a child, revealing to People magazine that she has started in vitro fertilisation (IVF) treatment with her boyfriend of two years, photographer Erik Asla.
The retired supermodel, 41, also vented about her frustrations at motherhood questions during the FABLife episode, stating, "I am so tired of seeing on my social media, 'Why don't you have kids? Why don't you have kids?' You don't know. You don't know what I'm going through."
Growing emotional, Banks continued, "When I was 23 years old, I used to tell myself, 'In three years I'm gonna have kids.' Then I turned 24. 'In three years I'm gonna have kids.' And then just every single year I kept saying that. And then, after a while it's like, OK, now I want to - and it's not so easy."
The full discussion will air in the U.S. on Monday (21Sep15).