At least three parties, including the pro-regime Palang Pracharath Party (PPRP), could be competing for the post of House speaker, for which each party is grooming potential candidates.
PPRP deputy leader Nataphol Teepsuwan said the party leader and secretary have assigned him to propose the name of the party's candidate.
Mr Nataphol spoke after he chaired a meeting to prepare the party's MPs for the first House session tomorrow, when a new House speaker will be elected.
Suchart Tancharoen, PPRP MP for Chachoengsao, said the party had picked him to run for the House speaker role.
However, his nomination would need to be made official when the formation of the new government becomes clearer. Mr Suchart served as deputy House speaker in 2005.
Political sources said the PPRP may be edging close to forming a coalition government, and they believed the name of the new speaker would give a credible indication of which party would lead it.
Also on Thursday, the Democrat Party mulled over four potential candidates for the speaker's role, according to a party source.
They are former party leaders Chuan Leekpai, Banyat Bantadtan and Abhisit Vejjajiva, as well as Therdpong Chaiyanant, a Democrat list MP.
When asked to confirm if his name had been put in the hat, Mr Chuan said he had no idea where the news came from.
He said the party has discussed the speaker issue. If the Democrat Party fields candidates, Mr Chuan said he was the most qualified among party members. Mr Abhisit was also a suitable choice, but he may not be interested, Mr Chuan noted.
Democrat spokesman Ramet Rattanachaweng said the party would hold a meeting, which could see the speaker nomination issue concluded, after the official opening of parliament today.
Pheu Thai leaders agreed Chiang Mai MP Sompong Amornvivat should be the party's candidate for the speaker post, said a party source.