The two clubs go head-to-head on Sunday and are set to do the same over Zaha, according to a report in The Daily Star.
Zaha, 19, recently signed a new deal at Selhurst Park but has been attracting a lot of interest from Premier League clubs.
Liverpool, Aston Villa and Stoke City have previously been linked with the £10 million rated star.
Managers Alan Pardew and Martin O'Neill are thought to have kept tabs on the youngster during his England Under-21 debut on Wednesday.
Source: DSG