The Pheu Thai Party is struggling to secure enough support from other parties for its prime ministerial candidate Srettha Thavisin.
It is now trying to woo support from the United Thai Nation Party (UTN), while the Move Forward Party (MFP) has apparently snubbed it.
The Palang Pracharath Party (PPRP), meanwhile, said it will support Pheu Thai's PM candidate.
Somsak Thepsutin, a Pheu Thai list-MP, refused to comment when asked if the Pheu Thai-led coalition needs to include the UTN and the PPRP.
However, he added: "Everything is possible. The new government wants to secure enough support to ensure stability."
The PPRP MP for Kamphaeng Phet said the party had not been approached by Pheu Thai since they last met for talks on July 23.
Pheu Thai on Thursday added the Chatthaipattana Party, along with its 10 MPs, into its bloc, raising the number of House seats held by the coalition to 238 out of the 500 total.
Earlier, Pheu Thai withdrew from the previous eight-party coalition led by the MFP.
Pheu Thai, which has 141 House seats, on Monday, teamed up with the Bhumjaithai Party with 71 seats. On Wednesday, it announced its coalition had six more parties.
Most MFP supporters do not approve of the party voting for a PM candidate from Pheu Thai, according to the MFP. It cited internal opinion polls by its MPs showing 95% of supporters are against such a move.
One MFP list-MP posted on Facebook the party must not open a door for the return of a dictatorship.
He was referring to the "uncle" parties: the PPRP led by Deputy Prime Minister Gen Prawit Wongsuwon, and the UTN, which has PM Prayut Chan-o-cha as its candidate.
