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."