The newspaper reports that the Gunners have also been scouting Porto winger Yacine Brahimi, but manager Arsene Wenger has decided that Zaha is a better option out of the two and a £35m bid could be made for the Ivory Coast international.
The Eagles star made an instant impact on his return from a knee injury against Chelsea in October, scoring in the 2-1 win over the Blues. He then secured a dramatic point for Palace against West Ham, scoring in the 97th minute to grab a 2-2 draw.
Brahimi meanwhile has also had an impressive start to the campaign with the Algerian international having scoring four goals and provided three assists in the opening 11 games of the league season. Like, Zaha, he usually plays wide on the left, but he is predominantly right footed.