The Ivory Coast international finds himself firmly in the transfer shop window heading into the summer.
His exploits across five seasons back at Selhurst Park have seen a man who flopped during a forgettable spell at Old Trafford between 2013 and 2015 rebuild his reputation.
A second stint with the Red Devils is now being mooted, while other leading sides in England and across Europe would welcome the opportunity to add the 26-year-old to their ranks.
Zaha is, however, tied to a contract with Palace through to 2023 and Hodgson believes that agreement will be honoured for at least another 12 months.
The Eagles boss said when quizzed on the latest round of exit rumours: “I have that old-fashioned idea that when you sign a contract, you go back after the season ends and start playing again.
“That’s the way I see it. I hope he finds good form in the last two games.”
Zaha struggled to make an impact in his most recent outing, as Palace played out a goalless draw with Everton.
Hodgson believes a mercurial talent can sometimes demand too much of himself, saying: “That pressure comes from him, not us. At times we encourage him to release the ball and run off it more, than run with it.”
Palace are eager to ensure that Zaha gets the chance to iron out his faults while still on their books next season.
Club captain Luka Milivojevic has added on the future of a talismanic presence: “If you play for Palace, you want him to stay.”
For now, Zaha’s focus is locked on ending the 2018-19 campaign as positively as possible.
Palace have just two games left to take in, away at Cardiff on Saturday and at home to Bournemouth.
They are destined to finish in the bottom half of the Premier League table, but still have the chance to clamber above London rivals West Ham and into 11th spot.