The Gunners saw a £40m bid rejected without hesitation by the south London outfit earlier this month.
The two clubs are some distance apart in their valuations of Zaha, but Arsenal boss Unai Emery is still keen on him.
But should the Ivorian be prised away from Selhurst Park, he would be in direct competition with Iwobi for his place in the team.
And the Nigeria international believes he may have to leave his boyhood club for pastures new if the sign Zaha.
“I am not one to chicken out. I have had it all over the years, being told I’m not good enough,” he told the Sun.
“So whenever the chance comes I always try and prove I should be starting.
“But it’s going to be difficult if Zaha comes. He will add more stress.
“I am up for the fight but the only time I would consider leaving is if I am not playing as much as I would like to.
“Obviously, my joy is to play football and not just sit out.
“If it comes to that I would have no choice but to leave.
“But I would always put up a fight to play — that is what I have done all my life.
“We have big stars already, so by adding another one I’ll just have to prove I can do better than them.”
Arsenal took their pre-season winning streak to three on the spin with a 3-0 defeat of Fiorentina last night.
Eddie Nketiah grabbed a brace and Joe Willock scored the third to put the Gunners top of the International Champions Cup table.
Emery’s side recorded an impressive 2-1 win over Bayern Munich and a 3-0 victory over Colorado Rapids previously.
Iwobi, meanwhile, has not yet returned to action since representing Nigeria at the Africa Cup of Nations in Egypt.