The Eagles boss addressed ongoing speculation surrounding his star player following the club’s 6-2 friendly defeat to Barnet on Tuesday night.
Zaha, who starred for the Ivory Coast during their AFCON campaign, has remained coy on his future, but last month his brother made a public plea for Palace to let him join the Gunners.
Arsenal swiftly launched a £40million bid, which was quickly rejected by the Eagles, who reportedly want closer to £80million for the winger.
Hodgson told Sky Sports: “I don’t think Arsenal have actually made a bid that has come anywhere near our valuation.
“I’m sure the player realises that if someone’s going to take him away from us, he’ll expect clubs to pay the market value.
“Until someone does that, there’s not much to discuss regarding Wilf.”
However, Hodgson confirmed that the club are willing to part with their prized assets, as long as the price is right.
Aaron Wan-Bissaka, who was named the club’s Player of the Year last season, recently joined Manchester United in a £50million deal.
“We would’ve loved to have kept him,” Hodgson said.
“But the bottom line is, when Manchester United come calling and they’re prepared to pay what the club feel is the market value of the player, then all we can do is wish him well.”