The Ivory Coast international had been hoping to head to pastures new during the summer transfer window.
Having previously flopped after joining Manchester United, the 26-year-old has rebuilt his confidence and form back at Selhurst Park.
A number of eye-catching performances have been produced for Palace, with 10 goals and as many assists recorded for the Eagles last season.
Arsenal were eager to buy into that ability at one stage, with Zaha opening the door for the club he supported as a boy, but no deal was done before the deadline passed.
Interest is expected to be rekindled in the talented forward in January, with Martyn conceding that Palace may need to reluctantly part with a prized asset so that he can fulfil his potential elsewhere.
"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.
"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.
"Premier League club’s finances are getting stronger and stronger and all that’s going to do is push prices up but there must be a price eventually that a selling club will take.
"Wilf is such an important part of Crystal Palace and played a big role in them maintaining their Premier League status these past couple of years so it’s difficult to let someone like that go. On the flip-side you don’t want him there if he’s going to struggle reaching the same level."
Zaha has been drafted back into Palace’s squad for 2019-20 despite making it clear that he wants out.
Roy Hodgson is prepared to keep picking the winger for as long as he remains at his disposal.