The announcement followed a meeting of the leaders of the eight parties and their members on Sunday morning.
Pita Limjaroenrat, leader of the Move Forward Party, said the meeting went well and progress was made in negotiations for selecting the next House speaker.
Chonlanan Srikaew, leader of the Pheu Thai Party, thanked Pita for demonstrating respect for Pheu Thai before explaining that there were many differences of opinion within his party.
As a result, Pheu Thai's negotiating team must present an agenda for discussion to the party's executive committee and MPs on Monday.
Pheu Thai will reach an agreement before noon on Monday and will then notify Move Forward and other parties in the coalition, Chonlanan said.
The agreement will be completed in time for the House of Representatives to vote on the next House speaker on July 4, he added, pledging that Pheu Thai will continue to work with the seven other parties in the Move Forward-led coalition.
Pita and Chonlanan both declined to answer questions about possible conditions in an agreement between their parties, including Phue Thai's support for Pita's bid to be the next prime minister.
They asked reporters not to create conflict between their parties.
Prachachat Party leader Wan Muhamad Noor Matha is willing to relinquish his bid to be a deputy speaker to make it easier for the eight coalition parties to form a new Cabinet, he said.
Move Forward and Phue Thai MPs will focus on the issues that are most important for the country and will not disappoint Thai citizens, Wan Noor said.
Thailand has already squandered almost nine years waiting for the return of democracy, he added.
Today's joint meeting of the eight parties also discussed their transition team's progress on critical issues, including energy, the digital economy, the cost of living, public healthcare, and education.
The transition team's working groups will develop a policy framework for the coalition to form a government and this framework will be announced in a statement to the National Assembly.
It will announce the policies that will be on the agenda for the next Cabinet to ensure smooth delivery of state services, Pita said.