It is understood the 23-year-old attack arranged a meeting with manager Alan Pardew on Thursday morning, where he made clear his wish to join Spurs.
Tottenham have started negotiations with Palace and are understood to be planning an opening offer of £15million.
Pardew is said to have refused Zaha’s request, and instead told the player he would speak to chairman Steve Parish and only sell if the price was right for the club.
Tottenham are keen to add another attacking midfielder to their ranks before the transfer window closes and Zaha, with his youth, energy and athleticism, fits the club’s, and Pochettino’s, transfer policy.
Meanwhile, Spurs also remain in talks with Marseille over a long-standing £11m transfer for Georges-Kevin Nkoudou, although it is understood their pursuit of the Frenchman will not be affected by their interest in Zaha.