Nigeria winger Iwobi was quoted by The Sun in the United Kingdom as saying Zaha's hypothetical arrival from the Eagles "would add more stress" in his battle for first-team minutes.
Iwobi added: "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."
Another British newspaper interpreted the comment as a warning to Arsenal, a claim the 23-year-old dismissed in a post to social media.
"Fake news and click bait! I don't know why some newspapers enjoy twisting words," Iwobi wrote on Twitter.
"I hope we sign world-class players and Arsenal progress as a team. I'm looking forward to the new season. Happy Sunday."
Arsenal reportedly submitted an unsuccessful £40 million ($71.9 million) bid for Zaha earlier this month, but neither club nor the player has confirmed anything, with Palace boss Roy Hodgson adding that he fully expected to be working with the Cote d'Ivoire star in the forthcoming season.
The Eagles star and attacker Iwobi would likely compete for similar positions as Unai Emery seeks to boost his options, but Zaha is said to be valued at £80 million ($143.7 million) by Palace.