Tony Tweedy apparently blames the language barrier between Cheryl and her French husband Jean-Bernard.
He also believes the six-month-old marriage is already effectively over - an allegation that JB has recently strenuously denied.
In quotes printed in The Sun On Sunday, Cheryl's cousin says that she and Jean-Bernard struggle to communicate.
Tony, 31, told the newspaper: "Cheryl can't speak French. I'm told he speaks little English.
"The family think the marriage is over. When I asked if Cheryl was happy with him, they replied, 'Put it this way, I'll give it six months'.
"That was three months ago, and look what's happening."
Reports about the state of their marriage have been circulating since November and the pair have not been seen publicly together since October.
It's believed the pair did NOT spend Christmas together after Jean-Bernard flew to Miami on business, leaving Cheryl in their shared home in London.
Cheryl celebrated Christmas Day with her family, but did not mention her husband in a festive post on social media.
Cheryl and restauranteur Jean-Bernard, 35, married in the Caribbean last July after a whirlwind three-month romance.
Last month, he was forced to deny their marriage was in trouble with he posted this message on Instagram: "Normally don't read or comment... But the truth is that even when my dad died I put my life on the line for my wife.
"Yes I am working like everybody else to put food on the table but my priority is my wife as this is the last person that is family.
"This is just nonsense. What matters is family and my wife is my only one left so if she need me I am always going to be there. My wife Cheryl is my priority nothing else."
Cheryl has so far declined to comment, however a source close to Cheryl did tell The Sun that she had not been in contact with Tony for years.
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