Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
Newspaper reports suggested United boss Sir Alex Ferguson held talks with the player in London on Sunday over a switch that could be worth up to £15m.
But Palace have told Sky Sports they have not given Zaha permission to talk with the Premier League leaders and no deal has yet been struck.
Arsenal and Tottenham are among others said to have been tracking the 20-year-old's progress, although United remain favourites to land him.