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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.