Meechai Ruchupan held talks with Prime Minister Prayut Chan-o-cha on Friday in a meeting that would help him decide whether to lead a panel drafting the new charter.
Mr Meechai and the prime minister met for the first time at Government House after his name emerged as a leading candidate to chair the 21-member Constitution Drafting Committee (CDC).
Both were tight-lipped after the meeting, with Gen Prayut saying only that he would disclose the decision on Monday after the National Council for Peace and Order meeting.
The prime minister, who returned to Bangkok from New York on Thursday night, said before the meeting he would show Mr Meechai a list of CDC candidates to help him with the decision on chairmanship.
"I'll show him the list for him to decide whether the names are qualified because he might have to work with them,'' the prime minister had said.
His remarks implied that other charter drafters might have already been picked although Deputy Prime Minister Wissanu Krea-ngam said on Friday that the members of the CDC and National Reform Steering Assembly will be announced by the Oct 5 deadline.
The deputy prime minister and another deputy, Gen Prawit Wongsuwon, have shortlisted CDC candidates to 40 for Gen Prayut to choose from.
A new team of drafters will have six months to write the new charter. Further delay in the process means, inlcuding a "no" national referendum, means Thailand will have to postpone new elections from next year to 2017.