Three bids in total were received, with the other proposals coming from the current owners — two companies run by Dundee businessman Derek Souter and his partners, called Union Street Developments and Union Street Properties — and another firm, LPT/Lola Ltd.
Souter and the city council have been in long-running discussions over the building for decades, to the extent a previous CPO was attempted in 1996.
The Egyptian Halls has had scaffolding around the site for at least 15 years, something Souter previously said was to protect the public.
If preferred developer status is granted next week, negotiations could start over a back-to-back agreement with Ediston.
This could see the council buy the building before transferring ownership to the Edinburgh firm.
Councillor Ruairi Kelly, the council’s convener for built heritage and development, said: “Identifying a compelling, detailed and well-progressed proposal for the Egyptian Halls is key to securing a future for this architectural masterpiece while giving new life and new purposes to Glasgow’s built heritage.
“By their very nature CPOs are lengthy and complex. But it’s important for Glasgow’s past — and its present and future — that we get this process right and bring this incredible building back to the heart of city life.”