The 35-year-old singer - who married the star in 2002 before they divorced in 2006 - has heard about his ex-wife's recent split from Tony Romo, but has no intention of rekindling their romance.
He said: "I think it's fun storytelling, but there's very little truth to any of it.
"I certainly have heard about her break-up and I wish her the best, as I've always done. Aside from that, there really is nothing to say."
Nick - who split from his long-term girlfriend Vanessa Minnillo last month - also denied rumours he and Jessica have been speaking to each other over the phone.
He said: "I haven't talked to her in probably two years. I wish her happiness. That's where it pretty much ends."
The former 98 Degrees boy band member also spoke about his recent love split, insisting he knows why his relationship with Vanessa failed.
He told People magazine: "I'm in a good place. I've learned, through years of not only being in this business, but being in relationships, that you have to take it as it goes. With every experience, you learn something about your life, and you try to Take That and move on and be a better person because of it. "We'll see what happens."