Arsenal have been linked with Zaha recently and have already had a £40m bid rejected for the Ivorian international as Palace demand a fee closer to double of what the Gunners have initially offered.
Should Arsenal sign Zaha, he will be competing for a place with Iwobi on the left-wing where Unai Emery usually deploys the Nigerian.
With reports also linking Barcelona’s Malcom and Everton Soares of Brazilian side Gremio to the Emirates Stadium, competition for places will be tougher than ever.
Iwobi, who is the cousin of former Nigeria captain Austin Jay-Jay Okocha, has promised to fight for his place in the Arsenal line-up but will not hesitate to leave the club if his first team chances are hampered by Zaha’s arrival.
“I am not one to chicken out,” the 23-year-old told The Sun. “I have had it all over the years, being told I’m not good enough.
“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.
“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’ve done all my life.”
Iwobi made 51 appearances in all competitions for Arsenal last season, scoring six goals.