While neither party has given an official reason, media reports suggested he was involved in a bust-up with Southgate's assistant Steve Holland.
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As far as I'm aware, he's not available to us," Southgate told reporters at Tuesday's squad announcement.
White was a near ever present for Arsenal at right-back this season, while he can also play centre half.
Liverpool youngster Jarell Quansah and Everton's Jarred Branthwaite earned call-ups to the squad.