The G1 building on George Square has been put up for sale and it is thought bidders will put in offers of at least £70 million.
As one of the city's most sought-after office addresses and home to celebrity chef Jamie Oliver's restaurant, there's already speculation that a number of big money offers will be tabled by investment fund managers.
The Victorian building in George Square was once the headquarters of the General Post Office but in 1969 became Glasgow's main post office.
It was axed by Royal Mail in 1995 and four years later was bought for £5m by city property developer Stefan King, owner of the G1 Group.
In 2005 he sold the building to Hamilton-based HFD Developments for more than £11m.
HFD chiefs then spent tens of millions of pounds on an upgrade which included retaining the A-listed Victorian facade and building a four-storey glass roof with panoramic views of the city skyline.
Celebrity chef Jamie Oliver had planned to open his first Scottish restaurant in Edinburgh but instead opted for GI's ground floor for an Italian eaterie.
The doors opened in summer 2010 and the chef admitted: "This is just a peach of a venue, and it's like a whole box of peaches for me."
The school dinners champion, who owns a chain of restaurants across the UK, said: "We are truly blessed with this location which I think is the best of all."
The nine-floor building is fully occupied and generates £4m per year in rents from a string of companies including Ernst & Young, a global leader in assurance, tax, transaction and advisory services, Mercer, Gardiner & Theobald and law firm Maclay Murray and Spens.
Another upmarket restaurant, Brown's Brasserie, also occupies the ground floor.
HFD's group development director Stephen Lewis said: "We have a net worth of more than £20m so we are effectively cash-rich and don't need to sell G1.
"But we are bowing to the inevitable because the building has generated so much interest from potential buyers.
"We are effectively bowing to that pressure although we are not quoting a guide price or a time scale for any sale. We will let the market decide."
A prestigious office development at 141 Bothwell Street in Glasgow was sold in January for £71m which has prompted the city's property specialists to predict that the historic G1 building – more than 132 years old – will be sold for more with the money to be re-invested by HFD into other projects.