Gold revealed during a question and answer session on Twitter that he expects the pair to remain part of Sam Allardyce's plans throughout the 2012/13 campaign.
Diame has been strongly linked with a January switch elsewhere, having shone for the Hammers since linking up with them as a free agent over the summer.
Carroll, meanwhile, is on a season-long loan from Liverpool, but it has been suggested that agreement could be cut short due to the striker's inability to steer clear of injury.
A switch elsewhere in the New Year has also been touted for the England international, which would bring an end to his stay in the East End.
Gold, though, has rubbished claims that a loan could be cancelled due to injury and when asked if Carroll will end the season with the Hammers, he said: "Yes, I believe so."
The Hammers supremo was later pressed on whether there was any truth in reports that Arsenal have expressed an interest in Diame.
He said: "I'm not aware of any offers."
He then went on to say 'I believe so' when asked if Diame would still be a West Ham player next summer.
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