Bosses at the shopping mall have already pre-let more than 20% of the units.
And it is hoped almost half of the 100 new stores will have been leased by October.
Earlier this month, the Evening Times revealed luxury chain Showcase Cinema de Lux had signed up to run a 10-screen cinema in the new extension.
The extended Galleries will deliver 1.2m sq ft of shopping, leisure and restaurant space and will be anchored by two major flagship stores.
They are a new 150,000sq ft Marks & Spencer and a reconfigured 300,000sq ft John Lewis department store.
A report to go before city councillors next week states: "Buchanan Partnership has exceeded the 20% pre-let target with strong interest from new to Glasgow brands."
The company is a joint venture between Land Securities and Henderson Global Investors.
Nick Davis, development director for Land Securities, said: "Glasgow is the biggest retail destination in the UK outside London and the interest that has been shown in the Buchanan Quarter and the extension to the Galleries highlights the continuing desire by retailers to come to the city."
He said the success of the new shopping complex opposite Buchanan Galleries in Buchanan Street is an indication of the demand to open up shops in the city.
Mr Davis added: "It is not showing any signs of letting up."
It is hoped initial work on the development will start in October this year with main works getting under way in January next year and finishing around Easter 2018.
Stuart Patrick, chief executive of Glasgow Chamber of Commerce, said: "The pre-let achievement of Buchanan Galleries' extension reflects on the overall strength of Glasgow's city centre."
Mr Patrick said the development will create almost 1500 jobs.
Liz Cameron, the council's executive member for jobs and the economy, said: "The interest from retailers underlines the faith investors are showing in Glasgow."