The first public exhibition to showcase the development was held in St Peter’s on Wednesday.
A new three-storey structure will replace an empty local authority building next to the heritage museum in Gainsborough Street, the birthplace of artist Thomas Gainsborough.
The project will provide spaces for exhibitions, displays and education, with four new galleries, including a showcase Gainsborough gallery – a landscape studio with panoramic views over Sudbury.
Architects for the project have been named as ZMMA, whose work has included projects at the Heath Robinson Museum and the European Galleries of the V&A, which won the Art Fund Museum of the Year last year.
Museum director Mark Bills said: “Thanks to the enormous support of so many people, Gainsborough’s House has now reached an important and pivotal point within its history, where there is a real opportunity to create a national centre for Gainsborough in Sudbury.
“We believe that reviving an artist’s birthplace will make a really positive impact on the town and we will be working to attract as many visitors as possible which, in turn, will lead to job creation and increased spend in the local economy.
“It will only happen if we can find the match funding and we still have a large gap to fill to create our vision. We need support now more than ever.”
The project secured £6.5 million from the Heritage Lottery Fund and private donors, but a shortfall of £2 million needs to be secured within the next year to keep the project on target.
If Gainsborough’s House secures the funds, building work will begin in autumn 2018 and will open to the public in 2021.
The public exhibition was the first chance for residents to see pictures and handle locally-sourced brick, flint and silk materials to be used in the build.