White, who was part of England’s squad for Euro 2020, is set to join Arsenal after the Gunners agreed a £50m deal with fellow Premier League club Brighton.
The 23-year-old has emerged as one of Mikel Arteta’s top transfer targets after an impressive season on the south coast and will bolster Arsenal’s defensive options following the departure of David Luiz.
But former England defender Mills says he is ‘surprised’ White is joining Arsenal instead of a bigger club and claims Man United should have entered the race for his signature.
Ole Gunnar Solskjaer wants to sign a new centre-back partner for Harry Maguire this summer but United are focusing their attention on Real Madrid’s Raphael Varane.
Mills told talkSPORT: ‘The only thing I am surprised at is Ben White has gone to Arsenal.
‘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.’
Asked why White would join another club, Mills responded: ‘Because he has got a better chance of winning things. What is he going to win at Arsenal? League Cup, if he is lucky. Maybe the FA Cup.
‘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.’
Arsenal legend Ray Parlour, meanwhile, believes White will be a good signing for Arteta’s side but admits his £50m fee will raise eyebrows.
‘He’s young enough and he’s a good player, he’s now in the England set up as well,’ Parlour told talkSPORT. ‘I think he’d be a decent signing but £50m is a lot of money.
‘I don’t know how much Arsenal have got to spend this summer. He will certainly be a good signing if they can get him, whether they can or not we will have to wait and see.
‘It’s a lot of money but if you want a player so badly… I don’t think his wages would be big.
‘So, over a five year period we aren’t going to give him the money that if you get an established star who’s in their prime, they’re going to have to pay him a lot of money in wages.’