The Pheu Thai Party, which is leading the move to form a new government, and its key ally, the Bhumjaithai Party, are at odds over when the cabinet portfolios should be allocated.
Pheu Thai insists that cabinet seats will be distributed only after the parliament votes in its prime ministerial candidate, but Bhumjaithai wants the issue settled ahead of the vote.
"After the vote for prime minister there will be discussions on the positions (in the cabinet)," Pheu Thai deputy leader Phumtham Wechayachai said on Tuesday.
He dismissed reports that prospective coalition allies were pressuring Pheu Thai to allocate them cabinet positions before the House and the Senate vote for a prime Minister.
Mr Phumtham reaffirmed that his party would nominate Srettha Thavisin to the parliament for prime minister, and his belief the party would have enough support from elected MPs and appointed senators to ensure his election.
He said Mr Srettha would receive support from MPs of many persuasions, including the Palang Pracharath Party (PPRP), other than the few parties that had announced they would sit in opposition.
PPRP agreed to join the alliance without any expectation of any cabinet position, according to Mr Phumtham.
He also said that Pheu Thai MPs were not concerned about the possibility of the party teaming up with PPRP and the United Thai Nation Party. PPRP has caretaker Deputy Prime Minister Prawit Wongsuwon as its leader and UTN earlier named caretaker Prime Minister Prayut Chan-o-cha as its candidate for prime minister.
However, Bhumjaithai Party leader Anutin Charnvirakul said on Tuesday the allocation of cabinet positions should be made clear before the vote for prime minister was taken.
He said he would discuss the issue with Mr Phumtham, Pheu Thai leader Cholnan Srikaew and Pheu Thai secretary-general Prasert Chanthararuangthong.
Mr Anutin said the talks would be constructive, so that all parties concerned could come to agreement. He expected the parliament would vote for prime minister next week.
Pheu Thai came second with 141 House seats in the May 14 general election. It walked away from its previous alliance with the election-winning Move Forward Party, which has 151 House seats.
Bhumjaithai came third with 71 seats and is Pheu Thai's biggest ally in its prospective coalition government, after the exclusion of Move Forward.