Smalling suffered the injury in training before the clash with rivals Liverpool at the weekend.
Nemanja Vidic is set to feature alongside Phil Jones for the clash with Olympiakos.
Rio Ferdinand could be set for a recall to the United team for the clash with Manchester City, as Vidic is banned for boths the clash with City and against West Ham.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.