The new prime minister is likely to be installed within the first three joint sessions of the House of Representatives and the Senate, scheduled for the next two weeks, said Deputy House Speaker-elect Pichet Chuamuangphan.
Mr Pichet said on Thursday that the three sessions were planned for July 13, 19 and 20, and they should provide enough time for the election of the new prime minister.
The coalition allies, consisting of eight political parties that favour Move Forward Party (MFP) leader Pita Limjaroenrat as the next prime minister, currently hold 312 votes in the House. The alliance will still need the support of 64 legislators to secure the 376 votes necessary to endorse Mr Pita, whose party won the May 14 general election with 151 House seats.
The constitution allows 250 senators to vote for the new premier along with 500 House representatives.
"The vote was initially set for July 13, but if it fails, there will be a second voting session on July 19 and a third round on July 20," said Mr Pichet, who is also the Pheu Thai Party MP for Chiang Rai province. "I think the three days should be enough to determine the prime minister."
Three sessions were planned at this stage due to the difficulty of scheduling a meeting with all the 750 members of both the lower and upper chambers of the House, said the Pheu Thai member.
When asked if Pheu Thai would lead the coalition if the three sessions fail to make Mr Pita as the prime minister, Mr Pichet said that would depend on the parliament and eight coalition parties.
"The eight coalition parties will comply with their MoU (memorandum of understanding) by continuing to stick together. There will be internal discussions and there should not be any problem," Mr Pichet said.
He also said that he was unsure how many senators would vote for Mr Pita. He said he had conversations with some senators who expressed their support for government formation for national development.