The Ukraine ace has missed the last two matches with a calf injury and he formed part of Arsenal’s squad for a warm-weather training camp in Dubai.
Zinchenko worked on an individual rehabilitation programme during his time in the United Arab Emirates.
Jakub Kiwior has started the last two matches at left-back but the Pole is more comfortable at centre-back.
But, with Takehiro Tomiyasu at the Asia Cup to represent Japan, Mikel Arteta is light on options at full-back.
Zinchenko had hoped to return in time to face the Eagles but the Evening Standard say he will miss the match as his recovery has been slower than expected.
Arsenal hope to have Gabriel Jesus back in contention, after he missed the FA Cup defeat to Liverpool earlier this month.
The Brazilian has formed part of the training group in Dubai and could go straight back into the starting XI.
For more stories like this, check our sport page.
Follow Metro Sport for the latest news on
Facebook, Twitter and Instagram.