The Ivory Coast international was the subject of a £40 million offer from the Emirates club earlier this summer, which was rejected.
"I don't think Arsenal have actually made a bid that has come anywhere near our valuation,” Hodgson told Sky Sports News.
"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."
Palace have already lost one key player this summer after Aaron Wan-Bissaka was sold to Manchester United in a £50 million deal.
"We would have 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.”
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