The new issue of Star claims they've wed, but Madden, 30, denies it on his band's website.
"I keep getting emails from old friends and family asking about a wedding. NO we didn't get married," he blogs.
Richie, 28, and Madden are parents to 1-month Sparrow and 21-month-old daughter Harlow.
Last May, they said they have no immediate plans to wed.
"I think for both of us, we are going to do it because we want to, not because that's what you do," Richie told CNN's Larry King. "We're going to do it when the time's right."
Added Madden, "We're really focused on our family, and we feel like -- we already feel kind of married, you know? Our family system that we have down, we feel like this is a real family and marriage, one day it will come."