The issue is hugely sensitive because the role is not hereditary and will not pass automatically to the Prince of Wales on the Queen’s death.
The Commonwealth has set up a “high level group” to look at the way the international organisation is governed.
This group is meeting later, officially to review how the Commonwealth is run by its secretariat and governors.
However, senior sources added that the gathering in London would also consider what happens when the Queen, who turns 92 in April, dies.
One said: “I imagine the question of the succession, however distasteful it may naturally be, will come up.”
The agenda for the all-day summit, seen by the BBC, says there will be a discussion of “wider governance considerations” which insiders say is code for the succession.
The group is expected to report to the Commonwealth Heads of Government Meeting (CHOGM) in London in April, which is likely to be the last that the 91-year-old monarch will attend.
A second source said the issue of the succession is expected to be discussed by Commonwealth leaders on the margins of the summit, particularly when they meet without officials “on retreat” at Windsor Castle.
The Queen was proclaimed Head of the Commonwealth at her coronation when she was head of state in seven of its eight members.
It is not an hereditary position that will pass automatically to her son, who will be head of state in only 15 of the 53 member nations that now make up the Commonwealth.
Any decision about the future would have to be made by the Commonwealth heads of government at the time of the Queen’s death. But there is no formal process for choosing her successor.
While many Commonwealth figures presume there will be no realistic alternative to Prince Charles, there has in the past been talk of electing a ceremonial leader to improve the organisation’s democratic credentials.
One source said the issue to be decided was whether a one-off decision should be taken to appoint Prince Charles to the position, or whether a new process should be agreed to ensure that it is always the British monarch who automatically becomes head of the Commonwealth.
“There are various formulas being played with,” the source said. “Should it always be the heir to the throne or Prince Charles himself? Is it the person or the position?”
The high level group, which is made up of seven senior former ministers from the Commonwealth, will meet at the body’s London headquarters at Marlborough House.
The group, which has its own staff and budget, is independent of the Commonwealth Secretariat. It will look at how the secretariat is run and funded, how a new secretary general is chosen and the balance of power between the Commonwealth’s governors and executive committee.
According to documents seen by the BBC, the high level group will not just confine itself to bureaucratic changes. The agenda for the meeting says: “Discussions will take into consideration the issues raised in the first session and also the wider governance considerations of the Commonwealth.”
The Queen has been working in private to try to ensure that Prince Charles does succeed her, sending senior officials around the world to lobby Commonwealth leaders.
At the last CHOGM in Malta in 2015, the Queen told them that she could not “wish to have been better supported and represented in the Commonwealth than by the Prince of Wales who continues to give so much to it with great distinction”.
The Prince of Wales represented the Queen at the CHOGM in Sri Lanka in 2013. A whole section of his website is devoted to the Commonwealth, noting that he has visited 41 out of 53 countries and has been a “proud supporter” for more than four decades.
The high level group consists of:
Chairman Anote Tong: Former president of Kiribati
Lord Howell: Former British energy secretary
Louise Frechette: Former United Nations deputy secretary general
Robert Hill: Former Australian defence minister
Dame Billie Miller: Former deputy prime minister of Barbados
Dr Ngozi Okonjo-Iweala: Former Nigerian minister of finance
George Vella: Former deputy prime minister of Malta