Arsenal have an agreement in place with Brighton to sign the 24-year-old centre-back for a whopping fee of £50m.
White is expected to undergo a medical with Arsenal once he returns from his holiday and sign a long-term contract with the Gunners.
Mills conceded that he is a brilliant signing for Arsenal but believes White could have done better than joining the north London club.
He feels the defender could have joined bigger clubs who have a better chance of winning trophies.
The former full-back is of the view White will not win anything at Arsenal or even get the opportunity to play Champions League football.
He believes at this stage of his career that White is too good for Arsenal and could have joined a better club.
Mills said on talkSPORT: “I think he is a great signing for Arsenal, he is a really good addition and he is an excellent player.
“I just wonder what his ambitions are?
“I am surprised that there aren’t bigger clubs who came in for him or better clubs who are more likely to win something.
“I look at Arsenal and probably Arsenal fans are probably steaming on Twitter or whatever, but are Arsenal going to win or even challenge for the title in the next two or three seasons? I think that’s unlikely.
“He is 24, so he is going to be heading in that two years of 26 and 27. He is not going to do a year at Arsenal for £50m and then leave.
“I don’t see him winning anything at Arsenal.
“I think he would have options of going to bigger clubs with a better chance of winning trophies, playing Champions League football, which would do his international career a world of good.
“I think he is better than Arsenal, he can do better than them.”
Arsenal finished eighth in the Premier League table last season and will not be playing any European football in the upcoming campaign. 0:13
