Liverpool, Manchester City, Tottenham and Chelsea are all said to be ready to bid for the former Manchester United forward this summer, after he nearly single-handedly kept Palace in the top flight this season.
Hodgson still has a soft spot for West Brom, and he says it will be hard on Sunday for himself and former Baggies favourites and current Palace backroom staff Steven Reid and Dean Kiely.
Crystal Palace signed off from an impressive Premier League campaign in a buoyant mood with a 2-0 win over West Brom on Sunday. "This is my home and there's no reason for me to leave".
"Obviously he's a London boy so hopefully he wants to stay in London and play and I think Palace would be the right club".
However, they have performed remarkably under the stewardship of Darren Moore, putting together their best unbeaten run of the season.
Israeli Singer Netta Barzilai Dubbed the victor of Eurovision Song Contest
I got a real kick out of the costume Israel's Netta Barzalai chose to wear to sing her song " Toy " at Eurovision . The previous Israeli to win was Dana International in 1998 with the song "Diva".
Crystal Palace must retain key players and buy quality additions to their squad if they are to improve on this season's Premier League performance, according to their manager Roy Hodgson.
The Ivory Coast worldwide scored four goals - including a brace in the 3-2 win over rivals Brighton - and registered an assist as Palace went unbeaten with two wins and two draws.
Earlier this week, Zaha was named the Premier League's Player of the Month for April.
Palace boss Roy Hodgson seems to have already accepted the possibility of the 25-year-old's departure, after having recently admitted: "It's inevitable we are going to lose a few good players in the summer".
"There is also Rubes [Ruben Loftus-Cheek] too and when we got those players back fit we have been a real threat".