White is set to join Arsenal this summer in a £50m deal following the arrival of Nuno Tavares and Albert Sangi Lokonga earlier this month. The England international is expected to replace David Luiz after the Brazilian left the club at the end of last season.
Liverpool and Tottenham were initially interested in the Brighton defender, but dropped out of the race as Mikel Arteta's side succeeded with their third bid for the 23-year-old. But Mills has questioned why White would want to join Arsenal.
“I think he’s better than Arsenal right now,” Mills told talkSPORT. “I just wonder what his ambitions are. I’m surprised bigger and better clubs with more of a chance to win something haven’t come in for him.
“I think he is better than that at the moment. What is he going to win at Arsenal? The League Cup if he is lucky. Maybe the FA Cup? It’s going to be a while before Arsenal win a Champions League. Winning the Premier League, you’re looking probably seven or eight years down the line, he might be retiring before that stage.
“I think he is an exceptional player and a fantastic signing for Arsenal, I’m just a little surprised Manchester United, who are looking for a centre-half, haven’t come in for him.”