Gold denied that the club have started making plans for next season without Zola, but also admitted there is a very real possibility that the 43-year-old could move on this summer.
"I have not spoken to, and am not speaking to, any other managers about taking over at West Ham," Gold told Press Association Sport.
"I haven't spoken to Franco since Sunday but what I do know is that he's preparing for the away match at Fulham (on Sunday).
"We have £3million of prize money to play for so we're concentrating on that. I'm going to the training ground on Friday as usual. I'll talk to him then. I hope he stays, but him leaving is a scenario, it is a possibility.
"He has had a tough time. He's had three years at West Ham and for a good part of that time he didn't know who was running the club. He's had bad luck as well.
"He could say I have done a fantastic job, I have got West Ham out of jail when I was given a chance and I have managed to go through all that and keep West Ham in the Premier League.
"He just might say 'I have done it, I'm exhausted and I'm going back to Sardinia.'"