Deutsche Bank has commissioned architect Sheppard Robson to design a 200 m structure that will deviate from the vertical by 20º.
The scheme, which is being developed by DGI, the property subsidiary of Deutsche Bank, has yet to be submitted for planning approval.
A planning officer for Islington council described the 50 m wide by 20 m deep tower as resembling "a slab of chocolate leaning on its side".
He said the leaning element sits on a 10-storey straight base and the tower straightens out near the top. The leaning section would comprise about 60% of the total structure.
He added the project has been on the cards since the middle of last year, but that things had gone very quiet in the past four months.
It is thought that CABE and the Greater London Authority will be in favour of the scheme and that English Heritage will have reservations based on its proximity to the City and conservation areas.
The planning officer said Islington council currently had a 30 m height restriction on new developments, but considered each application on its merits.
John Napier, project architect with Sheppard Robson, said the practice had been careful to consult CABE, the GLA and Islington council to ensure the design was acceptable.
The tower is to be located on the fringe of Islington at Ropemaker Place, near Moorgate, and is the latest in a series of proposed tall buildings for London, including London Bridge Tower and Heron Tower.
Napier declined to speculate on the chances of the project going ahead, although he said much would depend on the decision on Heron Tower, which has become a test case for tall buildings in the capital.
Structural engineer for the Deutsche Bank tower is Waterman and M&E engineer is Roger Preston & Partners.
At Tuesday's meeting of a DTLR committee on tall buildings, Peter Rees, city planning officer for the Corporation of London, said Deutsche Bank was "actively considering" relocating its headquarters.