In a question-and-answer session on his Twitter account, Gold insisted that the pair will be at Upton Park until at least May, despite reports linking the duo elsewhere.
Diame, who joined as a free agent, has been interesting Arsenal after impressive recent displays, and Goal.com revealed that the east London club are ready to offer the midfielder a renewed deal to stave off interest from the Gunners.
The on-loan striker has been less successful this term and the Hammers are considering sending Carroll back to Liverpool in January, after several uninspiring performances and recent injury troubles.
|IRONS GET HAMMERED|
|16/1||West Ham are 16/1 with PaddyPower to be relegated from the Premier League this season|
However, Gold replied to a question concerning whether Carroll will be at West Ham for the entire season by saying: "Yes, I believe so."
When asked about the interest Arsenal have shown in Diame he said: "I'm not aware of any offers."
Gold also said he believed the former Wigan man would remain at Upton Park for the remainder of 2012-13, responding "I believe so" when asked if the midfielder was happy to stay with the club.
The former Birmingham executive also revealed that Ricard Vaz Te is set to return from a shoulder injury in January.