The document shows owners Land Securities and Henderson Global Investors still intend to press ahead with a project which they have been trying to get off the ground for several years.
According to planning documents filed with Glasgow City Council, the development will add around 400,000 square feet of floor space to bring Buchanan Galleries up to one million square feet, incorporating restaurants, a cinema and more shops.
It will extend the centre towards Queen Street Station and involve a revamp of the station car park on North Hanover Street.
Overall car-parking capacity is likely to be reduced by 400 spaces to 1700 because of the changes.
A bridge across Cathedral Street will connect the station to the extended mall and there will also be a new entrance to the Royal Concert Hall.
The application for planning in principle is another move forward in the project since Glasgow City Council's £80m tax incremental financing (TIF) deal to back the development received final approval by the Scottish Government in the autumn.
TIF allows councils to fund infrastructure by borrowing against future business rate income which should be generated by a project.
The public money is expected to unlock around £300m of private sector investment for the scheme.
If full planning permission is granted before the end of this year, work would begin in 2014. The development is pencilled in to open in 2017.
In a trading update published yesterday, Land Securities said its development at 185 to 221 Buchanan Street remains on course to open on March 22 and is 99% pre-let, with tenants including Gap, Forever 21 and Fat Face.
It has also struck a deal with Google to use its product search service, which allows consumers to check online to see which retailers stock particular products and check prices.
The service is being rolled out along with wi-fi across all Land Securities' malls, including sites in Livingston, Aberdeen and Dundee. The property company said the move is to help retailers "execute multi-channel strategies" within its shopping centres.
The number of units in administration across its retail portfolio has risen from 1.8% at the end of September to 2.2%, due to the failures of HMV, Blockbuster and Jessops.
The overall occupancy in the retail portfolio stands at 97.1%, with like-for-like sales of retail tenants between October and December said to have been 0.3% up. There was £10.8m of development lettings booked in the quarter with a further £16.4m in the hands of solicitors.
Retail voids increased slightly from 3.1% to 3.2% while the London portfolio saw voids go from 2% to 2.4%.
Katherine Armstead, senior portfolio manager for Land Securities in Scotland, said: "All our centres remained resilient over the Christmas period with sales across the portfolio up more than 4%. Our shopping centres in Glasgow, Aberdeen, Dundee and Livingston remain thriving with high retention levels and below average void rates."