"Everyone was involved in the decision making. Nobody is precluded from it," said the 73-year-old.
"A second bid is possible. He is one of the players we are looking at.
"We'll have to wait and see what happens on that. The player is a favourite of mine.
"He is a young British player who we like but having said that, sometimes deals don't work out and you have to move on."
West Ham are planning a summer of rebuilding with Gold promising to "push the boat out" on "quality" players.
Co-owner David Sullivan said on Tuesday that West Ham would consider offers for all their players apart from captain Scott Parker - something Zola also claimed he was not made aware of.
"If I was Mark Noble or Rob Green or Valon Behrami I wouldn't be very pleased to listen to that," said the Italian.
"I didn't know that it was something like this but it's OK. We have been through so many things we are going to get through this as well."
Gold said on Thursday Sullivan's comments had been misinterpreted and assured worried fans he wanted the Hammers' best players to stay at the club.
After struggling to avoid relegation this season Zola's position at West Ham has been questioned.
The Hammers effectively secured their Premier League safety on Saturday with a 3-2 victory over Wigan but several managers, including Martin Jol, Steve McClaren and Mark Hughes, have been linked with Zola's job.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.