The Blues want more time to prepare for what could be the first leg of a tie against Barcelona or AC Milan if they beat Benfica in the last eight.
Chelsea's FA Cup semi-final will take place on Sunday, April 15, just three days before a potential Champions League clash.
Liverpool will feature in the other last-four FA Cup match on April 14 because they are allowed not to play on the anniversary of the Hillsborough disaster.
Chelsea, who face Benfica in the first leg of their Champions League quarter-final this evening, feel the FA should also be prepared to make a special case for them to play on the Friday night to help them in their quest for European glory.
Caretaker manager Roberto Di Matteo said: "I feel we should get more help from the FA over fixtures.
"Absolutely we need it because it doesn't help English teams in the Champions League.
"Benfica played Friday night before our game, so did Napoli before both matches in the last round.
"Their leagues try to give them a lot of help and the best possible advantage.
"We are engaged on this matter, but ultimately someone has to make the decision."
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