A report says the leader of the Tongan Human Rights and Democracy Movement, Akilisi Pohiva, is seeking a meeting with the Crown Prince to talk about positions in Cabinet.
The movement holds eight of the nine people's representatives seats in parliament after last week's election.
The King has promised to appoint two of these nine people's representatives to Cabinet.
But Mr Pohiva has told the Australian Associated Press that the movement wants more details before it accepts the proposal.
The news agency reports that the government is understood to want by-elections to fill the vacancies created by the proposed cabinet appointments.
But it reports Mr Pohiva as saying if a commoner is sacked from the cabinet he should be able to return to the parliament as an MP.