The Beady Eye frontman - who has been accused of allegedly fathering a seven-month-old girl with New York Times journalist Liza Ghorbani - is said to be "sick of the drama" and feels his relationship with wife Nicole Appleton isn't worth the battle.
A source told The Sun on Sunday newspaper: "Liam says he's had enough of it all - he's sick of the drama and doesn't think his marriage is worth fighting for anymore.
"He's very emotional because he's had no sleep for four days and been drinking heavily. But that's how he feels at the moment.
"Maybe when things have calmed down and he meets up with Nic he will have changed his mind. But for now he's telling everyone that's it."
Nicole's mother Mary said Liam only told her daughter about the claims the day before they appeared in a newspaper, and she was left "absolutely devastated".
She said: "That was the first Nicole heard of it. There was absolutely no indication it was coming. She's absolutely devastated.
"He's known about it all along and didn't tell her a thing, that's what is most upsetting to us.
"She found out when everyone else did. Nicole is in bits. They haven't spoken since he called her and told her what happened the days before it was in the papers."
The former All Saints singer's mother also revealed her daughter is "frightened" for the couple's future.
Speaking to the Sunday Mirror newspaper, she said: "My daughter's whole world has suddenly collapsed.
"I don't know what's going to happen. Nicole has just said to me, 'I'm frightened'. It's a horrible mess."