White has refused to be selected by the national team, as he does not get along with assistant coach Steve Holland.
England coach Gareth Southgate admitted he was told by Arsenal sporting director Edu of White's decision.
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"Arsenal defender Ben White has jetted off to Dubai," Stelling said on talkSPORT.
"He decided he didn't want to play for England in the games against Brazil and Belgium.
"He has been enjoying his time there by the looks of it, whilst his England teammates suffered a 1-0 defeat to Brazil, Ben was enjoying a game of UNO and soaking up the sun on a beach in Dubai.
"I have a bit of sympathy for people who play cards, but not Ben.
What are you doing? What are you doing posting the fact that you are in Dubai playing cards? You decided not to play for England, that's fine. Your prerogative, just let the boys get on with it."