The much-anticipated showdown could therefore see both teams unable to field their main striker, following the ankle injury to Wayne Rooney in Munich on Tuesday.
Drogba has sat out the last two days of Chelsea training after picking up a knock.
Fitness battle: Didier Drogba may not be fit for Chelsea's match against Manchester United
Drogba, who has 30 goals for his club in all competitions, missed last weekend's thumping 7-1 win over Aston Villa with Carlo Ancelotti blaming fatigue and an accumulation of bumps and bruises for his omission.
Ancelotti would prefer to have Drogba to call upon as his side strive to replace United as Premier League leaders. But as the performance against Villa showed, Chelsea look far more dangerous when playing with a lone striker.
Anelka was given the evening off against Portsmouth last week as Chelsea romped to a 5-0 win, with Drogba helping himself to a brace.
Sharp shooter: Didier Drogba scores for Chelsea at Portsmouth last week
And although Anelka did not get on the scoresheet against Villa, the France international looked much more dangerous than when stuck out on the right of an attacking trio.
Seven of Anelka's 12 goals for his club this season have come when not playing alongside Drogba in attack, including two which came in Chelsea's other seven-goal rout against Sunderland in January.
Even so, Anelka's failure to find the net since scoring the only goal against Burnley two months ago is a cause for concern and is sure to have Ancelotti crossing his fingers that Drogba recovers in time for Saturday's lunchtime kick-off.
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