Lloyd's distinctive 1986 building has been put up for sale by the German commercial property fund specialist Deka.
The reported price tag is £245m.
The property was designed by Richard Rogers Partnership and built between 1979 and 1984. It was officially opened by the Queen in 1986.
The building has a gross floor area of nearly 600,000 sq ft and Lloyd's occupies two thirds of the space.
Deka is expected to make a profit of at least £65m from the sale.