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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.