Some members of the National Reform Steering Assembly (NRSA) and the National Legislative Assembly (NLA) have called for appointed senators to be given the right to nominate a non-politician for prime minister.
At the same time, Prime Minister Prayut Chan-o-cha has said he will not be a candidate unless there was no one else suitable.
NRSA spokesman Wanchai Sornsiri on Wednesday proposed that the draft charter be changed to allow appointed senators to nominate a candidate for premier from outside political parties.
Voters decided in the Aug 7 referendum to allow senators to elect the next prime minister in conjunction with MPs. Therefore they should share the same right with MPs to nominate a candidate, regardless of whether the candidate is from a political party list, Mr Wanchai said.
"It is the desire of the people to have their elected representatives and people from other parties, including the security sector, to jointly reform the nation and develop it smoothly during the transitional period," he said.
"They must join hands with the hope that in the next five years the country will be heading in the right direction with sustainable and internationally recognised democracy which will be introduced," he said.
The Constitution Drafting Committee and the NLA must change the draft charter to suit people's desire, he said.
Seri Suwannapanont, head of the NRSA's political reform committee, supported the call, citing the people's decision on the additional referendum question.
NLA vice president Surachai Liengboonlertchai also backed the idea.
"The intention of the additional question is to ensure the continuation of national reform. We must consider solutions to some problems in advance so that the CDC can change [the draft constitution accordingly]," he said.
Some NLA members had proposed from the very start to allow senators to nominate a premier candidate, he said, and had spoken about it when they presented the draft charter to the people.
Prime Minister Prayut declined to be drawn on the idea. He told reporters to pose the question to legal experts.
He also sidestepped comment on former national reform councillor Paiboon Nititawan's plan to set up a political party and nominate him as the next premier.
"It is not the time. Do not raise it now. I will not give an answer. Otherwise, it will create a conflict with others," he said.
"I will not speak about it. It is not the time. The moment of the elections has not come. I will not answer," Gen Prayut said.
"I think there are many better people in the country than I. You should look to them. Unless a good person cannot be found, then you can talk to me," the prime minister said.
