The Walbrook building is being put up for sale by property investment firm Delancey.
Estate agents Knight Frank and CBRE have been briefed on the sale, which is expected to raise around £500m, according to Property Week (£).
Delancey bought the building from Minerva in August 2011 in a joint venture with Ares Management for £200m.
A number of potential investors have reportedly expressed an interest in the building, which sits near Cannon Street station. Designed by Foster and Partners, it is one of the City's largest and most iconic buildings.
“We are in discussion with a select group of global investors that may or may not lead to a sale,” said a spokeswoman for Delancey.
Current tenants include Worldpay, a payment processing company, Vanguard, the American fund manager, and gym chain Virgin Active.
The building is now almost fully let, but had difficulty attracting tenants when it was first purchased due to the dampening effect of uncertain economic conditions on demand for office space among financial sector firms.