But he has played down an Instagram video of him happily pointing at a huge "Zaha to Arsenal" sign in a nightclub.
Zaha's friend Anthony Billing, who posted the scenes in his Instagram story, also claimed later it was "just a joke" that the Ivory Coast frontman was unaware of.
Having initially claimed the message was from him and Zaha, Bollings wrote: "I can confirm that @wilfiedzaha had no partake in the banter last night.It was just a joke that I decided to go ahead with."
And Zaha himself posted: "I'm just enjoying my time off and can't control everything anyone does."
Anthony Billing on Instagram story, on holiday in a nightclub with Crystal Palace forward Wilfried Zaha. [IG story: anthonybilling]— afcstuff (@afcstuff) August 9, 2020
Zaha is seen pointing at a sign in the nightclub, ‘Zaha to Arsenal’. #afcpic.twitter.com/N1VBnkOJvV