The east London side were named as the preferred bidder for the stadium on December 5 last year and have been in talks with the London Legacy Development Corporation ever since about a potential move.
And Gold has now confirmed that, after months of negotiations, an agreement is drawing near.
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"As we speak I'm being promised March 16th. We would sign the agreement then."
The LLDC board preferred the Hammers to League One side Leyton Orient, as well as the UCFB College of Football Business and a consortium linked to Formula 1.
The board are set to meet on March 26th, but an extraordinary general meeting could be called if an agreement over the £429m venue is reached before that date.
"I'm embarrassed because I've tweeted 10 times that it's going to be next week or next month and here's a date," Gold added.
"The date comes and goes and then I give another date, but I think we are close."
Negotiations with the LLDC include talks on West Ham's share of the costs of converting the Olympic venue, and retractable seating set to be installed for Hammers matches.
"We will only go there if it's fit for use," said Gold.
"I won't go there if I have to look over a running track, but I believe that we are in a once-in-a-lifetime opportunity, let's face it.
"They've built a stadium, albeit wrong shape and size."