The Sun says he has been told he faces two months out with a knee injury.
Crystal Palace club doctors fear the result of scans today will confirm that he will miss crucial games in the relegation run-in.
The results will be assessed with club medics and manager Roy Hodgson today.
Zaha, 25, has complained of a knee injury but Palace fear it may be far more serious than first thought.
He missed a chunk of games at the start of the season, but remains Palace's most important player.
The Eagles have also been dealt another blow after keeper Julian Speroni was ruled out for the rest of the season with a knee ligament injury.