The city's oldest surviving restaurant, Rogano was founded in 1935 when the Queen Mary liner was being constructed in the Clyde and it shares the ship's elegant art deco style.
It has proved popular with politicians and celebrities ranging from Henry Kissinger to Tina Turner, Bob Dylan and Madonna.
Spirit has owned the restaurant for five years but decided to sell after conducting a review of its estate following its reacquisition by Punch Taverns.
"We feel that this wonderful institution will be better suited in the hands of an entrepreneurial restaurant operator," said Spirit.
Property agent Alan Creevy of Creevy LLH anticipates strong interest from both major UK operators and overseas entrepreneurs.
The property occupies a prime site near both the fashion retail and central business districts of Glasgow. Along with the 50-seat main restaurant, the business incorporates the 30-seat Oyster Bar, the 45-seat Café Rogano and a 20-seat private dining area.
It achieved sales of £2.29m in 2005, split equally between food and drink.
By Angela Frewin