Signing Zaha has been Gunners boss Unai Emery’s No.1 priority in the summer transfer window.
The north Londoners put in a £40m bid but the winger, but it was dismissed as derisory by the Eagles.
Starsport understands that Arsenal have a total of just £45m to spend on incoming transfers.
So unless Emery can shift high earners off the wage bill or sell players, they will struggle to buy Zaha.
And according to Sky Sports, sources close to the Ivorian say there are growing doubts about the likelihood of reaching an agreement.
It has been suggested that the Emirates outfit were preparing a second offer, which would include cash and players.
Calum Chambers, who impressed on loan at Fulham last year, was mooted as one star who could be incorporated into a deal.
But the Sky Sports report adds that Palace have no interest in taking any players from the Gunners.
Zaha, 26, is a boyhood Arsenal fan and is understood to be keen to play European football yet also remain in London.
Earlier this month, Zaha’s brother Judicael said: “Wilfried will always hold Crystal Palace and their fans in the highest regard.
“All the support they have given means the world to him.
“But it’s my brother’s dream though to play for Arsenal.
“Given all that Wilfried has given to Crystal Palace to help them remain a Premier League club.
“I hope Palace will be able to see their way to agreeing a deal with Arsenal that allows Wilfried to realise his dream of playing European football for the club he’s supported since childhood.”