John Lewis, Harrods, House of Fraser and Harvey Nichols are understood to have held discussions about opening at Edinburgh Airport.
The Edinburgh Airport site is currently occupied by World of Duty Free, but is set to go up for tender.
The retail space will occupy 17,200 sq ft after a relocation of airport security to a newly built extension.
An Edinburgh Airport spokesman said: “We are speaking to a number of interested parties regarding the availability of this space and we expect to start the formal tender process next month.”
It is believed the tender could be worth £50m based on the value of the revenue the store will generate over the contract period.
John Lewis and Harrods already have airport stores, but House of Fraser and Harvey Nichols are yet to launch one.
House of Fraser is in the process of an international expansion programme after opening its first store outside the UK last year in Abu Dhabi.
The department store retailer is to make international a key pillar of its expansion under its new Chinese owners Sanpower, who bought it in April for £480m.