'She tried to ban him from playing it, the final straw was apparently when she went mental about it and chucked it across the room.
'Liam loves to escape like other guys do, play online with the lads and all that, but by the end it was the Xbox or Cheryl.'
The source added that since the split, Liam is now back online playing FIFA, Call Of Duty and Grand Theft Auto.
The One Direction heartthrob has made no secret he is an avid fan of Xbox, having attended a Microsoft event for the games console in the USA in November last year.
MailOnline has contacted Liam and Cheryl's representatives for comment.
Last week, Cheryl confirmed she and Liam had sadly split in a tweet addressed to her seven million Twitter followers.
She wrote: 'We are sad to announce that we are going our separate ways. 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.'
Moments later Liam shared the same tweet with his own followers on the micro-blogging site.
According to The Sun, the couple mutually agreed to separate a fortnight ago following months of speculation regarding the state of their relationship.
A source told the publication: 'Cheryl and Liam worked really hard on their relationship – they had troubles earlier this year and were able to get through them.
'But they're in different stages of their lives and, after a lot of careful thought, came to a decision that it's best for everyone if they do go their separate ways.
The announcement came little more than 24-hours after Cheryl celebrated her 35th birthday, a milestone party Liam failed to attend despite flying back to the United Kingdom earlier that day.