The incumbent, Pohiva Tu'i'onetoa, has pulled out and there are now two contenders.
The caretaker education minister, Siaosi Sovaleni, is facing 'Aisake Eke, who won re-election last month after losing in his seat in the 2017 poll.
RNZ Pacific's correspondent, Kalafi Moala, said it appears that Mr Tu'i'onetoa is backing Dr Eke - hoping he will continue to follow the policies of the previous government.
Nominations for Tonga's prime minister close next Tuesday.
Mr Tu'i'onetoa became prime minister following the death of 'Akilisi Pohiva two years ago.