Reports have claimed Zaha is determined to leave Selhurst Park five years after he returned to the club from Manchester United, initially on loan.
Zaha struck 10 Premier League goals last term and has been linked with Arsenal and Everton, but Palace reportedly values its star man at £80 million ($143.7 million) having already lost young star full-back Aaron Wan-Bissaka to United for £50 million ($89.8 million).
Hodgson is not expecting Zaha, who helped Cote d'Ivoire reach the quarter-finals of the Africa Cup of Nations, to be sold by Palace.
"He has not spoken to me. I don't know if he's spoken to the club [about leaving]," Palace boss Hodgson said.
"As far as I'm concerned, he is coming back, he is our player and I've been given no information that the club is interested in selling him at the moment.
"I'm just expecting him back, looking forward to working with him and seeing some of the things he can do for us.
"I think he has got another 10 days or another week of holiday. I think he is back after we play Bristol City [on 28 July AEST] and before we play Hertha Berlin [on 4 August AEST]. That gives him his three weeks off.
"If he wants to come back earlier we will be very happy to see him."
After reports emerged claiming the 26-year-old had asked to leave Palace, Zaha posted a cryptic message on Twitter that read: "Whatever happened to speaking facts?
"It's sad and annoying how anyone will just open their mouth and speak on things or situations they know absolutely nothing about."
That came after Zaha's brother, Judicael, told Sky Sports it was the forward's "dream" to play for Arsenal, urging Palace to sell its prized asset.
Hodgson's side opens its 2019-2020 Premier League campaign at home to Everton on 11 August (AEST).