The French center back is close to securing a move from Real Madrid, as only the completion of a medical is required for him to put pen to paper on his contract.
United and Real confirmed an agreement for the 28-year-old to move, while Varane is expected to sign a four year deal with the Red Devils.
"You just don't know with foreign players coming in," Mills said on talkSPORT.
"He's had his injury problems – when you look at his average he plays around 20 games a season in LaLiga.
"Ten years there and 210 league games, so he's obviously had his injury concerns.
"A lot of those games are against seriously inferior opposition. This not the standard of the Premier League, robustness or intensity of the Premier League.
"I'm not doubting whether he's a fantastic player but I'm just questioning whether he'll be able to cope with the rigours of the Premier League.
"We've seen lots of players come in and haven't managed to do it – even Manchester United players – [Juan Sebastian] Veron, [Radamel] Falcao, [Angel] Di maria, [Memphis] Depay, [Diego] Forlan, [Bastian] Schweinsteiger, [Gerard] Pique.
"You even look at Deco, [Andriy] Shevchenko and [Gonzalo] Higuain [at Chelsea] – they didn't do it. [Alvaro] Morata, [Fernando] Morenties.
"They couldn't adapt, but they're not bad players, they just struggled to adapt to the Premier League."
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