ODM party Raila Odinga has said a referendum could still be held this year.
Raila says Kenyans can still vote before the year ends provided protective measures are put in place.
He said he is hopeful that the country's coronavirus peak will be in September thereby cooling off by end of October, allowing for planning for a referendum in November.
"So we are thinking we may be in a position to do a referendum by end of November or sometime in December," he said during an interview with NTV.
The push to amend the Constitution is centered on the Building Bridges Initiative process which has made a raft of proposals to alter the structure of governance. It has proposed the creation of the prime minister's office with two deputies.
The BBI task force chaired by Garissa Senator Yusuf Haji completed writing its final report on June 30 and has been waiting for President Uhuru Kenyatta and Raila's availability so it can be presented.
Some politicians have said the window of a referendum in 2020 to implement BBI recommendations is slowly shutting.
Lugari MP Ayub Savula told the Star on the phone that while the country was expected to hold the referendum this year, “several factors have come into play that will not make it easy to have one this year.
“Before coronavirus came in March, it was clear we would hold a referendum to amendment the Constitution, but with the cases increasing every other day and the challenges that come with it, the chances of a referendum this year are narrowing,” he said.
The country's confirmed cases stood at 24,411 cases as of Thursday with 399 fatalities.