A previous draft was rejected in September by a now-defunct National Reform Council. Some critics called the draft "unconstitutional" and fear a repeat.
A second failed draft would give the army additional room to prolong its stay in power, say analysts.
"The difference between this time and last time, however, is there might be more restlessness on the parts of political parties, especially if the army fails to show them how they fit into their long-term governance plans," said Ambika Ahuja, Southeast Asia analyst at Eurasia Group.
"The army's main goal is still to prolong its stay in power for as long as possible."