The Move Forward Party (MFP) and the Pheu Thai Party may consider a new power-sharing proposal when they hold talks on Thursday to negotiate over the role of House speaker, a source said.
One possibility is Pheu Thai will give up one cabinet seat in exchange for the House speakership, meaning the party will take 13 cabinet posts and the House speaker role while the MFP will get 15 cabinet seats and the prime minister's position.
It is unclear which post they might be prepared to sacrifice.
Under Pheu Thai's original proposal, the two parties would be allocated 14 cabinet seats each, with the MFP entitled to the prime minister's position and Pheu Thai taking the House speaker role.
The new terms are expected to be raised to end the stalemate over the House speaker post as parliament is set to convene next week, the source said.
Both parties were originally scheduled to thrash out the issue on Wednesday, but the MFP postponed the meeting indefinitely after Pheu Thai on Tuesday insisted on its demands.
MFP deputy spokeswoman Pakamon Noon-anan told reporters of the postponement on Tuesday night and added the planned meeting of all eight coalition parties scheduled for Thursday was also put off.
However, reports emerged on Wednesday that both parties will meet on Thursday and expect to iron out their differences soon. The eight-party coalition would meet on July 2.
The House of Representatives will convene on July 4 to select a speaker and two deputies after His Majesty the King presides over the state opening of parliament on July 3.
The source at Pheu Thai said both parties may have to make concessions to end the stalemate.
Pheu Thai has to carefully weigh the option of letting go of a cabinet post in exchange for the House speakership and be sure the trade-off is worth it before moving forward.
Srettha Thavisin, a prime ministerial candidate of the Pheu Thai Party, said on Wednesday that no matter how the matter is resolved, the political partnership between the two parties would carry on.
He said the MFP and Pheu Thai are working toward the same goal of setting up an eight-party government and the dispute settlement should not be seen as a "sacrifice" or "backing down".
Mr Srettha said he sees nothing wrong with the MFP candidate for the House speaker post sharing his vision and there is no such thing as "losing face" if the MFP does not get the post.
MFP MP for Phitsanulok Padipat Suntiphada, who is named as the party's candidate for the House speaker job, expressed confidence an agreement would be reached by the time parliament opens.
He would prepare the party for the House speaker role because negotiations are not finalised.
He called on the media to let the negotiating teams work, when asked about the possible breaking up of the partnership.
Stithorn Thananithichot, director of the Office of Innovation for Democracy at King Prajadhipok's Institute, said the contest over the post indicates Pheu Thai has a back-up plan in case the MFP fails to form a government.
In the event that the MFP ends up in the opposition camp and Pheu Thai is in government, Pheu Thai could face hiccups in the House, he said, adding the issue could still sever their relationship.
Wanwichit Boonprong, a political science lecturer at Rangsit University, said the parties might have to renegotiate if they cannot agree on the current proposal.
He said the MFP could encourage Pheu Thai to settle by offering one of the key cabinet posts, adding Pheu Thai has several factions and may be interested in getting an extra seat to appease its MPs.
Thai Sang Thai Party leader Khunying Sudarat Keyuraphan, one of the coalition allies, urged the parties not to let the people down and to quickly reach an agreement so their coalition government could be formed.
Meanwhile, Capt Thamanat Prompow, Palang Pracharath Party MP for Phayao, on Wednesday denied reports that he would nominate Pheu Thai list-MP and ex-deputy House speaker Suchart Tancharoen for House speaker.
He said he has no business in the matter although he respects Mr Suchart.