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) on its findings in London in April.
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 a hereditary position that will pass automatically to the Prince of Wales, 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 Charles, there has in the past been talk of electing a ceremonial leader to improve the organisation’s democratic credentials.
According to documents seen by the BBC, the high level group will not just confine itself to bureaucratic changes.
The agenda for the meeting is reported to say: “Discussions will take into consideration the issues raised in the first session and also the wider governance considerations of the Commonwealth.”
The high level group is said to consist 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; and George Vella, former deputy prime minister of Malta.