The right-back has not featured for the Three Lions since that tournament, refusing call-ups.
White has asked not to be selected for England for the foreseeable future, which manager Gareth Southgate has respected.
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Southgate explained: "Clearly on form I can't sit here and say he doesn't deserve to be in.
We had a call from Edu (Arsenal's sporting director) last week (and he) said Ben didn't want to be considered for England squads at this time.
"For me that is a great shame. He is a player we took to the Euros, a player we took to the World Cup and I spoke to him post-Qatar because I wanted to pick him."
Per The Athletic, White and Holland had a shouting match in Qatar when Holland felt that White was not listening to him.