I have learned that John Connolly, the company's new chairman, has appointed the headhunting firm Spencer Stuart to identify a number of heavyweight independent directors.
The new recruits are expected to replace Lord Condon, the former Metropolitan Police Commissioner, and Bo Lerenius, the former boss of Associated British Ports.
Both men have served on the G4S board since May 2004, and are expected to step down once they have completed nine years in their roles (after which they are no longer deemed to be independent for corporate governance purposes).
My disclosure that Mr Connolly has begun searching for new board members comes as the Olympic Games officially get underway with tonight's opening ceremony.
G4S has faced intense criticism for failing to provide thousands of security staff, a fiasco that the company has said will cost it up to £50m.
Nick Buckles, the chief executive, has received backing from some institutional shareholders but may yet end up having to quit following the Games.
The board of G4S has said that it will conduct a review of the contract, which I understand will be assisted by either Ernst & Young or PricewaterhouseCoopers, the accounting firms.
A G4S spokesman said: "The board has discussed the Olympic contract review and agreed that it should be supported by an independent external consultancy. At this stage no appointment has been made."