Move Forward and Pheu Thai, the two largest parties, may agree in principle to rewrite the constitution, but the latter is not expected to push for a quick revision that could prompt an early election.
Both parties carry the election promise to deliver a new charter.
Most political parties see the current constitution as being flawed as it was drafted on the orders of the now-defunct coup engineer, the National Council for Peace and Order (NCPO).
Former Pheu Thai leader Dr Cholnan Srikaew said on Aug 2 -- when he still held the post -- that the charter amendment must be prioritised as a top national agenda item.
He blamed the constitution for creating obstacles to forming a new government and sowing the seeds of a national crisis. The coup-appointed Senate serves as a case in point, as it is allowed by a provisional clause in the charter to co-elect a prime minister.
Critics argue that since the senators were not elected, they should have no role in this decision.
Dr Cholnan said the first meeting of the new cabinet would discuss whether to organise a referendum on the desire for a charter amendment, as well as the establishment of a charter-rewriting body composed of elected members.
He said once the charter has been overhauled, a general election would be called.
During the four years of the Prayut Chan-o-cha administration, efforts to amend the constitution proved an exercise in futility.
Some senators and coalition parties asked the Constitutional Court to rule on whether parliament could rewrite it in its entirety.
In 2021, the charter court declared that two criteria must be met before this could happen.
Specifically, two referendums must be held -- with the first one asking people if they want the charter amended. If the first referendum is approved, a second would follow to let people decide on whether to give the new version the green light.
One political pundit who declined to be named said Pheu Thai would be incentivised to delay finishing any redrafting of the charter, a process that is already estimated to take two to three years.
Once the rewrite is complete, the Move Forward Party (MFP) is likely to pile pressure on Pheu Thai to dissolve the House and call for a snap election so the new constitution can be implemented.
Other coalition parties seem to be on the same page as Pheu Thai on the need for a rewrite, but they advised against rushing the process.
And most are vehemently opposed to changing the definition of Thailand as a single, indivisible kingdom with a democratic regime and the King as the head of state, or any challenges to the lese-majeste law or other royal prerogatives.
Yutthaporn Issarachai, a political scientist at Sukhothai Thammarat Open University, told the Bangkok Post that Pheu Thai has a better chance of pushing through a charter rewrite than the MFP, which is seen as too radical.
He said any amendments would therefore be limited.