Payne, who shares 1-year-old son Bear Payne with Cole, has not responded to the rumors aside from the initial statement they both shared on Sunday.
"Cheryl and I are sad to announce that we are going our separate ways," the former One Direction member tweeted. "It's been a tough decision for us to make. We still have so much love for each other as a family. Bear is our world and we ask that you respect his privacy as we navigate our way through this together."
For months, Liam and Cheryl faced tabloid speculation that their relationship was on the rocks. In March, the "Get Low" crooner opened up about their less-than perfect personal life.
"You know, we have our struggles," the 24-year-old confessed to ES magazine. "Like, of course I'm not gonna sit here and say that everything's absolutely fine and dandy, because of course you go through different things, and that's what a relationship is."
He explained, "This part of our relationship was never not going to happen; there was always going to be a little bit of tenseness in the way we sort ourselves out. But tell me a relationship in the world that doesn't go through a spot like that? It's about whether you make it through or not, together, is the main point there, I guess."
The exes went public with their romance in late 2015.