The Building Bridges Initiative Taskforce announced on Monday that it was yet to compile its report and that a decision on a referendum had not been made.
Chairman Yusuf Haji, who is Garissa Senator, said that contrary to reports in the media, the team was still collecting views from the public - he said the remaining eight counties will have been handled by August.
"The remaining counties are slated to present their views within the next three weeks beginning Tuesday," Mr Haji told a press conference in Nairobi.
He added that the team's decision will be based on the opinions of Kenyans, not politicians'.
The 14-person team was formed following the famous May 9, 2018 handshake between President Uhuru Kenyatta and Orange Democratic Movement leader Raila Odinga.
It has been going round counties gathering views on policy and administrative reform proposals and is expected to handover a comprehensive report by October 23.
The taskforce is poised to recommend fundamental reorganisation of the country's governance structure.
So far, the team has received memoranda from institutions and individuals and has held nine public hearings with stakeholders at the Kenyatta International Convention Centre in Nairobi.
Information on a preliminary brief to President Kenyatta and Mr Odinga, which the Nation is privy to, reveals immense support for that route as informed by overwhelming submissions.
The team has been regularly briefing the two on the progress and is expected to retreat at the end of the month to draft the final report before its term ends in September.
At the press conference, the team's Vice-Chairman Adams Oloo emphasised said the taskforce had not made a decision on whether there will be a referendum for constitutional changes.
Dr Oloo reiterated that the report will not be influenced by political leanings.
"Let politicians say what they want in political rallies. That is not our position. Our position will be on what is tabled during the sessions across the country," he said.
The two addressed journalists accompanied by officials including Taskforce Joint Secretary Paul Mwangi.
Several politicians, including Bungoma Senator Moses Wetang'ula (Ford Kenya party leader), have given their views on the outcome of the team's work.
Earlier in July, Mr Wetang'ula warned that Kenya could face turmoil if the 2022 general election is conducted under the current constitutional framework.
He accused the BBI team of delaying to come up with a blueprint that would give the country direction and said a referendum should be conducted by next year so that inclusivity is entrenched as part of efforts for cohesion.
Busia Senator and former Attorney-General Amos Wako, who is a member of the team, promised that at the end of its term, the taskforce will present a balanced report capturing Kenyans' aspirations on cohesion, government and constitutional reforms.
Mr Wako also said the report will not be affected by political leanings or individuals as some people fear.