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That's according to Danny Mills who says the Brighton defender should have set his sights higher than the Gunners.
After starring last season, White is expected to seal a £50 million switch to Arsenal - with an official announcement imminent.
However, the 23-year-old's proposed move to Arsenal has been questioned by Mills, who reckons he should have gone to a genuine Premier League title contender.
He reckons Man United should have tried to sign him. Of course, Ole Gunnar Solskjaer is looking to snap up Real Madrid's Raphael Varane.
"Let's assume that he will be at Arsenal for two or three years at least before he goes somewhere else. I just think he is better than that.
"What is he going to win at Arsenal? League Cup, if he is lucky. Maybe the FA Cup."
Mills continued by hailing White, he added: "I think he is an exceptional player and I think he is a fantastic signing for Arsenal.
"I am just a little bit surprised that Manchester United, who are looking for a centre-half, haven't come in for him."
White made his name on loan at Leeds, where he starred at the back under Marcelo Bielsa - helping them win promotion to the top flight.
He enhanced his reputation last season, with the England international in line for a big summer move.
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