Zaha is keen to leave Selhurst Park and fancies a move to the Gunners, the club he supported as a boy.
But Palace have made it clear he is going nowhere now that Aaron Wan-Bissaka is on his way to Manchester United.
Wan-Bissaka is poised to join United in a deal worth up to £50m – and the Eagles will not let another big star leave.
Arsenal are interested in Zaha and know he would like to join them but any chance of them signing him now looks remote.
Palace value the Ivory Coast international at around £80m – way over Gunners boss Unai Emery’s whole summer budget.
It was assumed that any move for Zaha would depend on Arsenal qualifying for the Champions League.
But while their failure to do so has not dampened the player’s enthusiasm for the move, it has left the club needing to raise money from sales to fund any realistic approach.
So for now Arsenal are pressing on with other targets, with an improved £20m offer for Celtic’s Kieran Tierney likely.
The Scottish giants have already rejected two bids of £15m and £18m for the Scotland star but a deal is still thought possible.
Arsenal are also locked in talks with St Etienne over 18-year-old defender William Saliba.
But the French club want him loaned back to them next season, which is proving to be a major sticking point.
Emery has been told he has less than £50m to work with unless he can boost his transfer funds by selling off players.
But while the club will listen to offers for big earners like Henrikh Mkhitaryan and Mesut Ozil, the pair have failed to generate significant interest.
Midfielder Lucas Torreira is wanted by AC Milan, and did little to dampen speculation about his future when he complained of finding it hard to settle in London.
But it is understood Torreira will not push for a move, and Arsenal do not want to sell a player they only brought in last summer from Sampdoria.
There is an acceptance at the club that every player has a price but they believe the 23-year-old remains happy at the Emirates and could play a key role for Emery next season.