The list of 21 new constitution writers will be known before Sept 23, when Prime Minister Prayut Chan-o-cha flies to the United States for the UN General Assembly meeting.
"For the chairman, I'm considering several people. He must be accepted by all sides. But importantly, will politicians accept him? I haven't decided whether the writers of the previous draft will be asked to join the new team," Gen Prayut said.
The cabinet and the National Council for Peace and Order (NCPO) will have a joint meeting on Sept 22 and the list will be discussed then, he said.
"In the meantime, all sides can propose candidates. Anyone can apply and I'll consider them myself," he said.
Asked by reporters whether the Nitirat group could join, Gen Prayut said: "They can apply but I doubt when the time comes they will join. Reporters said earlier they didn't want to be reform councillors or charter writers. In any case, I won't invite them. They need to apply if they want to. I won't beg them."
Nitirat is a group of Thammasat University lecturers well known for its pro-democracy and anti-coup stand
The group's name was floated as a candidate by reporters because Worachet Pakeerut, a core member of the group, is among the few public-law experts in the country who have yet to serve the junta.
The PM also ruled out Amorn Chantarasomboon, a former secretary general of the Council of State, as chairman of the new charter drafting committee, saying he was sick.