Hodgson expects Zaha to stay at Crystal Palace despite Chelsea rumours
Zaha hit nine goals to help Palace stay in the Premier League last season and has been linked with a move to Chelsea, having reportedly rejected a new contract.
The club are said to have turned down a bid of £30million plus midfielder Danny Drinkwater from Chelsea and are rumoured to want £70m for the winger, who rejoined the club on a permanent deal in 2015 after failing to make the grade at Manchester United.
It has been claimed Zaha has told his team-mates he wants to leave but Hodgson has denied the speculation.
"I don't read those stories to be perfectly honest, they circulate all the time," Hodgson told talkSPORT.
"I spoke to Wilf yesterday and he certainly gave me no indication it was true about wanting 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 world where I speak to the players and watch them train rather than follow what is happening in the mass media.
Waiting for the start of the season like... #CPFC #GodIsGreat pic.twitter.com/xIPUxoTWL2
— Wilfried Zaha (@wilfriedzaha) August 1, 2018
"The thing with Wilf is very simple. He's very much an integral part of our plans.
"Everyone likes him. Everyone admires him, he knows that and I think he likes and respects the club as well.
"So, my hope and my plan absolutely is that he will stay. I'll let the speculation continue and I will continue happy to work with him."
Speaking in May amid reported interest from Manchester City and Tottenham, Zaha indicated he would not push for a move from Palace, which he described as his "home".
But Allardyce, Palace manager during the 2016-17 Premier League season, thinks the time is right for the increasingly versatile Ivory Coast international to move on from Selhurst Park once more.
"He's ready because of the experience of Manchester United and then coming back to Palace and re-establishing himself as a top player," former England manager Allardyce said to talkSPORT.
"A few years have moved on and he's established himself even more as one of the most talented players in his position in the league.
"The last two seasons, in particular, have shown his maturity, and his end product has got better. He's not only played out wide, but Roy has used him through the middle successfully.
"It's London, where he prefers, so he'd be more comfortable there. So, as much as I don't like to say this to Crystal Palace fans who I love, it is probably time for Wilfried to move on, and get that next challenge under his belt.
"I do think the fee would have to be much bigger than what Chelsea are talking about."