Architect Avery Associates has been working up a design for the site known as 1 Undershaft, which would see the existing building replaced with a sloping sided skyscraper rising to almost 270m.
The unique profile of the building has already prompted one contractor to dub the building “The Fang”.
A spokeswoman for the architect said: “It is very early days and a planning application has not been submitted yet.
“We have come up with a scheme that is sympathetic to the surrounding buildings.”
The architect has aimed to preserve the views of the nearby Gherkin with a building that has sloping sides and mirrors the Cheesgrater tower on its other side.