Spurs were understood to be interested in the 25-year-old in January too, but ultimately failed to prise him away from Selhurst Park.
Crystal Palace remain reluctant to lose their star player but could be forced to sell at the end of the season, particularly if they suffer relegation from the Premier League.
The Eagles currently sit just one point above the relegation zone and see Zaha as integral to their hopes of staying in the top flight, despite the Ivory Coast international currently being sidelined by a knee injury.
Zaha is expected to command a fee in excess of £50m as his current contract runs until 2022, but that price tag has not put Tottenham off and, even with the January addition of Lucas Moura, The Mirror reports that Spurs are lining up a new approach in the summer.
Zaha has scored four goals and registered one assist in 20 Premier League appearances this season.