The People's Representatives in Tonga say the next Prime Minister should be one of them.
A nominated candidate for the Prime Minister's post must have majority support among the 26 representatives.
The nine representatives of the nobility are understood to be backing the caretaker Minister of Internal Affairs Lord Vaea as their candidate.
However an independent representative Siaosi Sovaleni says they don't support such a move.
The independents have met the nobles and 10 members of the Democratic Party.
"When we met the nobles we expressed the fact that we'd like a member of the People's Reps to be the next PM. They had a proposal and we had a discussion and then we parted to actually consider each others proposal. The same thing happened with the, (Democratic), Party whereby we actually met to actually have a discussion on what their needs are and actually express what our thinkings are."
The leader of the Democratic Party 'Akilisi Pohiva has indicated he is interested in the role of Prime Minister.
Mr Sovaleni says the independents will decide next week if they will nominate their own candidate.