Tottenham had a long-standing interest in Zaha before he signed a five-year contract last summer, and Hodgson admits clubs may move for the winger when the transfer window opens.
When asked whether he expects there to be interest in Zaha, Hodgson said: “He is an obvious name but there are other players, too. I would not be surprised if other players were wanted or thought could be good additions. We have to be prepared for that.
“If offers come along for players who are doing well for us that we are not particularly anxious to lose, decisions will have to be made by the club as to what offers are to be turned down and what offers are to be accepted.”
Zaha has been in good form since he returned from a knee injury last month, scoring three goals in five games.
Palace are bottom of the Premier League and have not won in five matches since they beat Chelsea 2-1 at Selhurst Park last month, but they are still just five points from safety.
Hodgson will be targeting a good points return from their run of three matches in a week against teams in the bottom half of the table.
Palace play Stoke at Selhurst Park on Saturday before away games at Brighton and West Brom next week.
Hodgson said: “The players feel the rewards for the previous five games in terms of points [Palace have drawn two and lost three] have not been matched with our performances.
“That should give us some confidence for this run of games between now and Christmas.”