After drawing 1-1 with Algeria after extra time, Wilfried Bony and Serey Die both missed penalties in a 4-3 shootout defeat for The Elephants.
Zaha played 94 minutes of the match before being replaced by Maxwel Cornet in extra time.
Arsenal have had a £40m bid for the winger turned down by Crystal Palace already this summer.
And they have since reportedly offered the Eagles their choice of three Gunners stars in a bespoke player-plus-cash deal.
The trio are defenders Carl Jenkinson and Calum Chambers and midfielder Mohamed Elneny.
But Palace value Zaha at over £80m and are not believed to be interested in a player swap.
Gunners boss Unai Emery could be banking on the 26-year-old downing tools in an attempt to force the move through.
With Zaha expected back at training in the near future, the attacker’s future will soon become clearer.
But Sky Sports man Kaveh Solhekol says Zaha’s camp are concerned Arsenal don’t have the funds to afford the Palace talisman.
“The latest information we have is that nothing will happen until Zaha is back from Egypt and has face-to-face talks with the Crystal Palace hierarchy,” he said.
“That needs to happen. But if the Ivory Coast make it to the final, that’s just a couple of weeks before the window closes.
“As far as Palace are concerned he’s not for sale but Zaha wants to move and Arsenal want to sign him.
“The feeling around Zaha’s camp, however, seems to be that Arsenal can’t afford him.”
Sky Sports reporter Dharmesh Sheth also added: “Wilfried Zaha, this one could be come to a head very, very, very soon.”
Meanwhile, Arsenal are reeling from the news that club captain Laurent Koscielny refused to travel on their pre-season tour of America.
The central defender wants to return to France with Bordeaux, who have offered him a three-year contract.
But the Gunners are refusing to let him leave for free and may strip him of the captaincy.