Architect SPPARC has drawn up the plan to build a 420,000 sq ft office and retail scheme at 1 Portsoken Street, just north of the Tower of London.
The plan would see the existing 1980s office building known as Lloyds Chambers demolished to make way for a new landmark 12-storey scheme with three basement levels.
Its rectangular floor plan would be softened with curved facades leading to it being named The Butterfly.
The plan has been submitted on behalf of Portsoken Investment, a joint venture between a group of private investors, by consultant DP9.