Reports of the player telling teammates he was keen to join the Blues and was considering putting in a transfer request emerged on Thursday. But Hodgson has since dismissed them, insisting that the player has so far given no signs he wants to leave Selhurst Park.
Zaha has rejected an offer of a new contract from Palace and it is believed that Chelsea are leading the race to sign him. Yet, according to the Eagles manager, a recent conversation with player seemed to indicate that he plans around next season.
"No, nothing at all I am afraid. I don't read those stories. They circulate all the time," Hodgson said to talkSPORT (H/T football.london).
"I spoke to Wilf yesterday and he certainly gave me no indication that was true that he wanted to quit the club, in fact we were talking about how good the new signings were and how they would help us.
"I'm afraid I prefer to stay in that mode where I speak to the players and watch them train rather than follow what is happening in the mass media, and all the stories that are circulating.
"The thing with Wilf is very simple, he is very much an integral part of our plans, and an integral part of Crystal Palace Football Club."
Hodgson also added that he understands why clubs are after the player this summer but he's hoping he continues on with Palace.
"Everyone likes him and admires him, he knows that and I think he likes and respects the club as well," the coach continued.
"And my hope and plan, absolutely, is that he will stay. I will let the speculation continue and I will continue to be happy to be working with him."
"He is a top, top class player and I am sure there are many, many clubs, not just in England, but in the world, who would like to have him."