The Gunners remain keen on recruiting the services of the England international despite signing Noni Madueke and Viktor Gyokeres, and he would be keen to move to North London.
However, Palace want his £68 million release clause activated, and Arsenal have had reservations about paying the full clause for the 27-year-old.
The Gunners will continue to keep tabs on Eze and will likely proceed with a concrete move for him if the Eagles should drop their asking price in the final five weeks of the summer transfer window.
Sales would also give Arsenal a considerable boost in his pursuit, with Leandro Trossard or Gabriel Martinelli options to be sold.
The Gunners are in talks with Nwaneri over a new contract, and negotiations are in the final stages as they look to secure his services for the long-term future.
That could be wrapped up very soon, which would allow them to focus on other things, but a move for Eze will now likely depend on outgoings or Palace agreeing to do business for considerably less than £68m.
The Eagles have reportedly identified Leicester City attacker Bilal El Khannouss as his potential replacement, but they could insist on getting top dollar for him.
The Gunners have spent £200m in recent weeks, with the recruitment of Gyokeres, Martin Zubimendi and Madueke costing almost £180m, and they may not have room to complete another big-money signing this summer.
Completing a deal for Eze will be huge as he is a game-changer capable of significantly improving their attack given his track record, and manager Mikel Arteta will be hoping things fall in place in the coming weeks.
