Ramos picked up the injury in Saturday's 5-0 La Liga win at Real Betis, which lifted Real to within a point of joint leaders Barcelona and Atletico Madrid.
"As of today he is not comfortable," Ancelotti told a news conference. "If he improves he'll play, if not he'll rest."
If Ramos is unable to play at Espanyol's Cornella-El Prat stadium in Barcelona, his place in the starting lineup will probably be taken by Nacho.
Real's France international Raphael Varane, another centre back, has been sidelined by a long-term knee injury but Ancelotti said he could return soon.
"He has recovered well. When I see he is ready to play he'll play. Let's see in the next 10 days."
This week's other Cup quarter-final, first legs are Barcelona at Levante and Real Sociedad at home to third-tier Racing Santander on Wednesday. Holders Atletico Madrid host Athletic Bilbao on Thursday.
(Reporting by Iain Rogers, editing by Ed Osmond)
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