The proposal would also see the town's existing library turned into a public archive.
The consultation will begin on 27 May and run for three weeks, with drop in sessions being held in the Dumbarton area.
Findings will be reported back to the next committee in August, when Councillors will make a decision on the future for the buildings.
Under the proposal, Glencairn House would include dedicated spaces for children and families, computer use and quiet study alongside a wide selection of fiction and non-fiction items in a variety of high-demand formats, a relaxing recreational space featuring a coffee station and improved physical access, enabling level access via the main entrance on the High Street, and internal lifts to each floor.
The historic three-storey building would have a new four-storey extension added to the rear with stunning views over the River Leven and Dumbarton Castle.
The museum facilities would include an entire floor dedicated to local history floor and incorporating an exhibition space. This would be further supported by displays of artefacts throughout all floors of the building.
Alongside the library and museum, the proposals would also turn the B-Listed building into a social hub, offering meeting and event spaces for community use as well as a flexible event area for exhibitions and public displays.
It would bring the library back to the heart of the high street, where it was originally located in the 1830s.
The current Dumbarton Library building on Strathleven Place would be transformed into a community collections store and archive and opened to the public. This new facility would, for the first time, enable access to the stored objects and documents in West Dunbartonshire's heritage collections.
Councillor Iain McLaren, Convener of Infrastructure, Regeneration and Economic Development, said: "This is a very exciting proposal which has really considered how Dumbarton's oldest building and current library building can both be put to their best use.
"Protecting the history and heritage of this area is hugely important so I'm glad to see officers have not only thought of Glencairn House but also considered a new sustainable future for the existing library building.
"I hope everyone takes the time to be part of the consultation in a few weeks, as the views of residents and community groups are extremely important and will shape the way in which this proposal can be taken forward."
(CM/JG)
