Directors would have to reveal whether they had served on the boards of companies that had gone into receivership or liquidation, and details of personal bankruptcy, unspent convictions and public criticism from regulators would also be disclosed.
The information would have to be published within a fortnight of a director's appointment. At present, such information is not published. It is recorded on cards that are sent to the Securities and Futures Authority, the City regulator, and is not available to the public or to investors.
The current system has been criticised for allowing companies to provide shareholders with only selective information about new directors.
When Lord Walker, the former Conservative Cabinet Minister, became a director of British Gas, the company's annual report failed to mention his previous link with Maxwell Communications.
Stuart Bell, research director at corporate governance specialist Pirc, said: "We are broadly in favour of attempts to increase transparency and disclosure. There are instances when only selected biographies are provided, certainly in annual reports. Anything that can bring pertinent information to investors would be welcomed."
The move is part of the Stock Exchange's campaign to improve corporate transparency and to provide valuable information for small investors. It follows an amendment to its listing rules in January, which required the publication of similar information about existing directors when companies offer new shares to the public.
The Stock Exchange is understood to have set out its proposals in a letter sent to all its 2,500 member companies. Companies have been invited to comment before final rule changes are published this summer.
Tim Melville-Ross, director-general of the Institute of Directors, said: "I have some reservations about revealing details of previous bankruptcies. In Britain, if you have been declared a bankrupt you are finished. But in the US, it's treated as part of being a businessman."