The retailer is said to be close to reaching a deal with property fund manager Frogmore to sell the mainly derelict site in the Merchant City where it planned to set up shop.
The sale would finally kill off an 11-year dream for Glasgow to have its own Selfridges.
The price is understood to be in the region of £5m.
Frogmore has owned several buildings in the same three-acre block for a number of years.
The company is said to want to build flats, a four-star hotel and shopping units at the site of the former Goldbergs department store.
In 2002, Selfridges bought the Glasgow site and talked about opening a 200,000sqft store at a cost of £90m, creating 1000 jobs.
But in 2010 Selfridges confirmed that it had no immediate plans to open in the city.
A spokesman for Glasgow City Council said: "Any planning application on this site will be considered in due course."
Selfridges and Frogmore declined to comment.