But Allardyce, Palace manager during the 2016-17 Premier League season, thinks the time is right for the increasingly versatile Ivory Coast worldwide to move on from Selhurst Park once more.
Zaha only committed his long-term future to the Eagles with a five-year contract last May to take his wages to around £100,000-a-week.
Hodgson, the veteran Crystal Palace chief, meanwhile, is confident about retaining Zaha for the upcoming term and shared what he discussed with the dynamic attacker recently.
Palace will not sell Zaha, unless they are offered a huge sum to part with him for a second time in his career.
And if Chelsea come in with a mammoth bid nearing Palace's demands, then they will reluctantly do business.
However, the 25-year-old attacker has been tipped for a move again this summer after rejecting an improved £125,000-a-week contract and the Ivory Coast worldwide has attracted interest from the upper echelons of the league with Tottenham and Chelsea linked in recent months.
The thing with Wilf is very simple.
But Spurs are now set to make a big splash in the transfer market by stealing Wilfried Zaha, a top target for their London rivials Chelsea.
"My hope and plan is that he will stay and I will continue being happy to work with him".
"That would lead to comments that we don't think he's good enough to play elsewhere".
Maurizio Sarri has snapped up midfielder Jorginho and third-choice goalkeeper Rob Green since replacing Antonio Conte in the Stamford Bridge hot seat but he too is expected to be active during the final stages of the window.
Chelsea suffered a humbling defeat to Premier League champions Manchester City in the Community Shield on Sunday and Sarri knows more signings are needed before Thursday's deadline.