The cabinet has nominated six experts from outside the government to sit on a committee vetting constitutional amendments.
The cabinet has a quota of 12 seats on the 49-member panel which will also comprise 18 MPs from the coalition parties and 19 representatives from the opposition camp.
The allocations are based on the make-up of parliament.
"Our six nominees are all outsiders, without anyone from the cabinet," Prime Minister's Office Minister Tewan Liptapallop told media on Monday after sending the list of names to the government whip.
But there may be a change to the list because some have rejected the invitation, he said.
"That's because the representatives were nominated without their knowledge," Deputy Prime Minister Wissanu Krea-ngam told media separately.
Mr Tewan is also preparing to discuss remaining six seats cabinet-allotted seats with the government whip.
"The [next six] nominees must possess sound knowledge of the constitution and, again, they must be experts from outside the government," he said.
However, the move upset some MPs.
"There should never have been a cabinet quota in the first place," Democrat MP for Nakhon Si Thammarat Thepthai Senpong commented, pointing to an interview with Prime Minister Prayut Chan-o-cha in which he said rewriting the charter is the job of the Lower House, not the government.
Mr Thepthai also strongly disagreed with an idea to give some seats on the panel to senators.
"This is tantamount to including those who would naturally oppose any amendment," he said, adding it would prompt accusations of a conflict of interests as one of the proposed amendments is reportedly to scale back the power of the Senate.
Some senators are former members of the now-dissolved National Legislative Assembly, the legislative arm of the preceding military-engineered government which approved the constitution before a referendum on Aug 7, 2016.