"It will be over (today)," said Souki (D, Wailuku).
The 39 Democrats from both sides have been anxious to have the 51-member House organized before Christmas.
The House reorganization has been stalled by 14 Democratic dissidents.
They maintain that their goal isn't necessarily to topple Souki but to decentralize power and get a House leader open to procedural reforms they are advocating.
"You will be seeing some reforms that were jointly agreed to that will now become House reforms," said Souki, who did not specify the changes.
Before yesterday's talks, Souki said he was confidant that he has the necessary votes to return as speaker.
According to the dissidents' count, Souki has 24 votes with Rep. Jun Abinsay (D, Kalihi) on the fence but leaning toward Souki.
The pact to have the reforms and the secret balloting in today's caucus instead of the usual open vote was apparently formalized yesterday during a series of closed-door meetings.
Souki and Rep. Ken Hiraki (D, Kakaako), a dissident leader, declined to provide details on how today's caucus was to be conducted.
But legislative sources said 26 votes won't be needed to elect a speaker.
Only a majority of the Democratic majority - 20 votes - will be necessary.
The House has 12 Republicans.
The dissidents have never publicly mentioned anyone as a challenger to Souki.
Before the start of yesterday's negotiations, Souki said he was confident that he has the votes to return as speaker.
But a secret ballot allows a Souki supporter to vote for someone else without Souki knowing.
Dissidents, who include Reps. Dennis Arakaki (D, Kalihi Valley), Alex Santiago (D, Pupukea) and Dwight Takamine (D, Hilo), have said a secret ballot allows fellow Democrats to vote how they really feel without fear of intimidation.