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.
It said the issue of the succession of the head of the Commonwealth was not part of the group’s mandate, but described the day-long discussions as “open”.
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 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.
The group said it was independent of the London-based Commonwealth Secretariat, and would report only to the heads of Commonwealth governments.
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 in 1953, when she was head of state in seven of its eight members.
Although the Queen took over from her father George VI, 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.