Zaha, 27, expressed his desire to leave last year and at the time, a source told ESPN that Arsenal had a £40 million bid plus add-ons rejected.
- Stream FC Daily on ESPN+
- Transfer Q&A: How will summer transfers work?
- Insider Notebook: Lampard loses faith in Kepa; Jovic's Real nightmare
When asked whether Zaha would remain at Selhurst Park, Hodgson responded: "That's the $64,000 question isn't it, that one, always but it's not just Wilf Zaha -- there's players in every club that come into that category.
"Wilf has made it clear, ever since I came to the club really, that he would relish a move and would like to move on and find some pastures new.
"But he's a very valuable player and the club realises his value and appreciates his value and so really everything will depend I guess -- as it always does -- [on] what sort of offers the club is going to receive for him and how they will equate that with the need to keep him or the need, maybe, to satisfy his wishes, and allow him to go after giving good service to the club for a period of time.
"Quite frankly, I've got no answer to that question, it will be all a matter, I guess, of seeing what transpires."
Zaha has been one of the standout players for Palace this season, contributing four goals and five assists in all competitions.
Palace valued Zaha around £70m last summer and when asked if Palace will demand the same asking price, Hodgson replied: "I think he should, because he's a very top-quality player.
"But, as I say, that will be a decision and matter anyway for [chairman] Steve Parish and the other owners of the club.
"They will have to take any offers into consideration and I'm pretty certain that I will be consulted and at the end of the day the final decision will have to be a club one."
Zaha left Palace to join Manchester United in 2013 but endured a tough spell at Old Trafford and returned to the London club on a permanent deal months later.