Governors are now seeking to abolish the cap barring them from seeking the same seat after serving for two five-year terms.
In a special committee chaired by Makueni Governor Kivutha Kibwana, the county bosses proposed that they should be allowed to seek re-election as many times as they would like to.
They argued that the system was being unfair to them by limiting them to only two terms yet MPs and MCAs were allowed to seek re-election for as many times as they wanted.
According to The Star, the draft document prepared by the committee on behalf of the Council of Governors sought a possible referendum in order to include their demands.
The proposal is, however, in its initial stage since the committee has only met once since it was constituted last year October.
The committee is co-chaired by Meru Governor Kiraitu Murungi and consists of Joyce Laboso (Bomet), Anyang' Nyong'o (Kisumu), Amason Kingi (Kilifi) and Charity Ngilu (Kitui) among others.
The Council of Governors chairman Wycliffe Oparanya, however, revealed that he had not seen the reports yet.
He further disclosed that after the report is forwarded to him, he would call for a retreat for all the governors in order to develop a united front when pushing for the changes.
Once the special committee, consisting of 11 members, completes its proposal, it will present it to the Building Bridges team.
This comes months after the CoG proposed for a referendum seeking to increase the state's allocation to counties from the current 15% of the audited budget to at least 45%.