Reports suggest the aid was granted with the understanding it would be used for a rooftop gallery that will house glassware, pottery and silver.
The entire refurbishment project now has a total spend of £15m.
National Museums NI Chief Executive, Tim Cooke, said he expected the museum, which is half way through works, to reopen in summer 2009.
"The project is on schedule and within budget.
"The new roof is almost complete, the building has been stripped back inside and the new layout is taking shape after major structural work.
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"Overhead walkways are under construction, the framework for the new Hall of Wonders has been erected and the galleries are being prepared for fit-out.
"The core of the landscaping work to re-model the relationship with Botanic Gardens is also advancing well," said Mr Cooke.
The museum's restructuring scheme includes a new entrance and arrival area, a new restaurant facility and modernised history and natural science galleries.
Mr Cooke said: "We continue to work hard raising funds in a challenging climate and if more money comes in the next couple of months we will continue to expand the project to make sure we make the most of this opportunity."
In addition to the anonymous donation, the museum has received funding from the Department of Culture, Arts and Leisure, the Heritage Lottery Fund and a number of other sources.
Staff at the museum have undertaken an outreach programme, while the attraction has been closed.
The workers have visited schools, libraries, science centres and local museums across the Province.
(PR/JM)
