The 25-year-old has a £3.5m buy-out clause in his contract, with both Arsenal and Tottenham thought to be interested in acquiring the Senegal international.
But, to the delight of Gold, the transfer window closed with Diame still at West Ham and the board member revealed that the club are now ready to offer him new terms.
"This was a difficult window for us," Gold told reporters. "We've had the concern of Diame leaving almost right the way through, so we are delighted that he is still here.
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|5/2||West Ham are 5/2 with BetVictor to finish in the top half of the Premier League
Thanks to Andy Carroll's winner in their 1-0 home win against Swansea City on Saturday, West Ham now sit nine points clear of the relegation zone and, with the return of several key players from long-term injuries, Gold has set his sights on a top-half finish.
Writing in Saturday's matchday programme, the co-owner observed: "It has been brilliant to see the likes of Jack Collison, Momo Diame and Andy Carroll back in the first team and they could be key to our run-in.
"I dropped in to see the guys in training and saw how determined they were to turn this run of results around.
"Despite the difficult January, I didn't see any division or cracks, only a willingness to work together to get some points on the board."