And Martyn believes he needs to join a club the size of the Gunners if he wants to play at the highest level.
“If a player wants to go enough and is desperate enough to leave then it’s possibly not in your best interests to try and keep him because you then have a player who doesn’t want to be there,” he told 888Sport.
“Not that Wilf wants to let the club down in any way. He loves Crystal Palace. He just wants a chance to further his career and go to potentially a bigger club like Arsenal.
"That’s the type of club he needs to move to. He needs a club that is challenging for the Champions League because that’s the standard that he’s at.
Wilfried Zaha wanted to leave Crystal Palace this summer (Image: GETTY)
Wilfried Zaha was the subject of a £40million bid from Arsenal this summer (Image: GETTY)
He just wants a chance to further his career and go to potentially a bigger club like Arsenal
Nigel Winterburn on Wilfried Zaha
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“I don’t see him lying down and not trying though. He doesn’t strike me as that type of person.
“He cares enough about his own club and will give his all until he moves on.”
Everton also tried to lure Ivory Coast international Zaha away from Selhurst Park but had two bids rejected.
Desperate to leave south London, Zaha ended up handing in a transfer request - which Palace rejected.
Nigel Winterburn believes Wilfried Zaha needs to join a club like Arsenal (Image: GETTY)
Roy Hodgson is happy Crystal Palace managed to retain Wilfried Zaha's services (Image: GETTY)
Crystal Palace chief Roy Hodgson is delighted the Eagles have retained Zaha’s services and is confident his performances on the pitch won’t wane in light of the club blocking his summer exit.
“Yes he’s staying," Hodgson said of Zaha. “Yep. Absolutely. We’re pleased about that, of course.
“He’s an important player for the club and we’re looking forward to him doing - this year, or this season - what he’s done for the last two seasons.”
Zaha and his Palace team-mates will be back in action on Saturday afternoon, travelling to Old Trafford to take on the winger's former side Manchester United.