Amani National Congress (ANC) leader Musalia Mudavadi is supportive of the creation of the prime minister office as part of a broader system of government.
Mr Mudavadi, a principal of the National Super Alliance (Nasa), said that had they formed the government, they would have ensured a review of the Constitution and created the position in line with the Bomas draft.
The other members of the opposition alliance are Bungoma Senator Moses Wetang'ula (Ford Kenya), Kalonzo Musyoka (Wiper Democratic Movement) and Raila Odinga (Orange Democratic Movement).
“Nasa had already committed to reviewing the Constitution and revisiting the Bomas draft where the parliamentary system was favoured alongside a broader structure of government," he said on Sunday at Redeemed Gospel Church in Outering, Nairobi.
"[This included] the position of the prime minister who would be accountable to Parliament, added Mudavadi, who served as deputy PM from 2008-2012.
Mr Kuria said the PM may vie as a member of the National Assembly who, if not elected, would automatically become a nominated member.
The ANC leader further called for an all-inclusive dialogue on the key issues that will become part of the referendum as the clamour for one gathers steam.
“It is important that we all sit as a nation, consult, separate and isolate the issues that are sensitive and need to be corrected and define the ones that will go to a referendum and those that can be dealt with without a referendum,” he said.
Nonetheless, Mr Mudavadi insisted that the Independent Electoral and Boundaries Commission (IEBC) must be reformed before a referendum as "we cannot go for a referendum with the same referee who has problems".
The IEBC has been on the spot over matters including spending, election preparedness and wrangles that have seen the departure of chief executive Ezra Chiloba and commissioners Roselyn Akombe, Paul Kurgat, Margaret Mwachanya and Connie Maina.
It is currently taking applications to fill the position of CEO.
Mr Mudavadi further said that the success of the BBI lies in its broadening inclusive to prevent disenfranchisement and the idea that it is only for President Uhuru Kenyatta and Mr Odinga.
“It should not be seen as an initiative of two people. It has to be broadened and made inclusive. Suppose one decided to pull back, what would happen? It should be formatted so it can be similar to the Bomas approach,” he said.
The politician further said all groups, including religious leaders, people living with disabilities and youths, should be involved.
"It is not about Musalia being at the table but about having everyone across the board," he said.
Mr Mudavadi warned those "using the handshake to close their eyes on pertinent issues affecting the country", saying accountability is needed.
“If we are fighting corruption let us do it because it is evil, not because of the handshake. People want to see more accountability, not people in an exclusive or elitist club. We must correct issues affecting the country,” he said.