Winner: Eberechi Eze
Arsenal Football Newsletter
Eze, whose £68million release clause expires on August 15, remains a target for the Gunners having held talks with the player's representatives earlier in the summer.
However, amid reports of an agreement between the two clubs, Standard Sport understands Arsenal may need to make space in the squad before finalising any deal for the England international.
Along with Eze, Palace captain Marc Guehi has been linked with an exit as Liverpool are said to be keen on signing the central defender who has less than a year remaining on his contract.
Speaking after the Eagles beat Liverpool on penalties to win the Community Shield at Wembley, Parish admitted it will be difficult to keep hold of both players.
He said: "Yeah listen, of course but players come and go in football clubs you know.
"I mean it's a life cycle isn't it you know. Hopefully they're still here, that's what I'd like but we'll see."
Eze played the full 90 minutes against Liverpool on Sunday and though his penalty was saved by Alisson Becker in the shootout, he was on the winning side at Wembley once again.
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Interestingly, a clip of the attacking midfielder after receiving his medal has gone viral on social media.
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As Eze walked back down the steps, he is asked - presumably by an Arsenal fan - if he will be making the move to the Emirates Stadium in the near future.
The 27-year-old did not give a response, but many eagle-eyed Gunners supporters noticed a wry smile as he made his way to continue the post-match celebrations.