The practice won the competition to extend and upgrade the existing grade II-listed Beaux Arts-style building back in 2005, seeing off the likes of Keith Williams.
However, the project stagnated while gallery chiefs moved to cement a funding package for the proposed works.
Now Swansea City Council has set a date to consider and potentially 'approve measures to allow funding for redevelopment' of the 1911 gallery.
The authority has already pledged £500,000 towards the proposals, which will see a new glass gallery, dubbed 'the last wing', built on to the building.
The rest of the funds for the development is expected to come through the Arts Council of Wales and the Heritage Lottery Fund.
As well as creating a new 'visible' wing, the scheme aims to overhaul the existing educational rooms and open up 'full physical access' to all the galleries, study spaces and exhibitions.