"Zaha hasn't been training to any great extent as we're nursing his knee problem that he has. We will have a look at him tomorrow and hope the knee will be OK," Hodgson told a news conference.
"We've had to be cautious after the Huddersfield game as he came back from injury much earlier than he should have done."
The Ivory Coast international missed friendlies against Togo and Moldova last week.
Defender Jeffrey Schlupp is also doubtful for the visit of Liverpool after he limped off early in the game against Huddersfield.
Crystal Palace are 16th in the table with 30 points from 31 games while Liverpool are third.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
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