Mills believes it will take time for the France international to acclimatize to the English game.
The former Lens man is on the verge of completing a move from Real Madrid to Manchester United after both clubs agreed on a deal.
Varane is one of the most decorated players in the history of football, having played on every biggest stage. The 28-year-old has won the World Cup, four Champions League trophies and three La Liga titles.
Many have suggested that the Premier League will just become another competition for the Frenchman but Mills believes it will not be a cakewalk for Varane.
‘We know his pedigree. We know he’s an exceptional talent,’ Mills told TalkSPORT.
‘Obviously often partnered in recent years alongside Sergio Ramos. It will take him a little bit of time to adapt certainly to Manchester, to Manchester weather. But more importantly the Premier League.
‘We know he’s won everything but he’s had one or two injury problems and he hasn’t played every single game, every single season – he’s had those injury issues in the last few years. I think it might take him a little bit of time to adjust to the robustness of the Premier League.
Varane spent ten years at the Santiago Bernabeu, playing 360 games in all competitions for Real Madrid. He also scored 17 goals, provided seven assists and won 18 trophies in the process.