The Hammers goalkeeper’s contract is set to expire this summer but Gold hopes Green will commit to Sam Allardyce’s cause following victory in the play-off final against Blackpool on Saturday.
"One of the first negotiations that will take place will be with Robert Green," Gold told BBC Sport.
"He is a world-class goalkeeper and his salary would be commensurate with that, but now that we are in the Premier League I am confident we can keep Robert."
|West Ham return to the Premier League
Green, who will travel with the England squad to Poland and Ukraine for Euro 2012, had been linked with move to Tottenham, but with West Ham’s quick turnaround in fortunes, Gold believes Saturday’s success can be enough to tie Green down to a new deal.
"There was no way we could keep Robert in the Championship in the second year after relegation by paying him his value," he continued.
And Gold, who shares ownership of the club alongside David Sullivan, confirmed that the situation of other West Ham players will also be reassessed ahead of the upcoming season.
"Some negotiations will start straight away and some will start in a few weeks," he said.
"A lot of contracts will be with players that go back onto Premier League wages now we have gone up."
Gold also reassured Hammers fans that manager Allardyce will be given funds to strengthen the squad in an attempt to prevent last season’s misfortunes which ended in the heartache of relegation.
He continued: "Once we've done all our negotiations with the players you want to keep, Sam will come to us and tell us the areas we are weak in and need to strengthen and this is what it's going to cost us.
"Until all those things have been sorted out you're not quite sure what you will be doing, but you know you have to strengthen your squad to give you the best possible chance of staying in the division."