Kiaran MacDonald, general manager of the adjacent Savoy hotel, which owns and operates Simpson's, said that a refurbishment of the restaurant - originally opened in 1818 as a chess club and coffee house - is long overdue.
"Simpson's remained untouched during the recent closure of the Savoy, so the time is now right to consider its future. It will always remain an integral part of the guest proposition for the Savoy, but we want to look at the possibility of whether or not to bring in a third party operator."
MacDonald said that the while the Grand Divan, the main dining room of Simpson's on the ground floor, is the jewel in the crown of the business, the building has untapped capacity for a total of up to 620 customers.
No decision has yet been taken as to whether the Simpson's name will be retained. "The Simpson's name has great value in the market place, based on its long history," added MacDonald.
The restaurant is renowned for its staunchly British menu and the carving at the customers' tables of joints of roast beef and lamb from an antique silver-domed trolley. Gerry Rae is the current master cook, the name the restaurant has always used in place of executive chef.
Chef-restaurateur Brian Turner spent two years at Simpson's in the early 1960s, during which he worked alongside Richard Shepherd, who later went on to own Langan's Brasserie. It was a time which he described as the restaurant's "hey-day".
"Every day we served up to 1,200 covers, having roasted 12 sirloins of beef and 20 saddles of lamb, a dozen ducks and a dozen chicken. The food we served was very simple, but it was always focused around a sensational meat product.
"It is an iconic restaurant and I really hope that its remains as a great British institution."
Davis Coffer Lyons, the leisure property specialist, is expected to draw up a shortlist of parties interested in leasing the Simpson's site over the next 90 to 120 days.