Ms Kemkaran previously said those behind the leak were “weak” and “foolish” to have committed an act of “treachery”, and that a “thorough investigation” had been launched.
She could face a vote of no confidence in the coming weeks over the leaked video, according to the Local Democracy Reporting Service.
The LDRS reported that a backbencher, who has asked not to be named, has already begun seeking the required number of signatures to spark the possible dismissal.
Councillor Anthony Hook, opposition leader of Kent County Council, has called Ms Kemkaran’s position “untenable” and said she is “unfit to lead”.
“If you thought the Conservatives were bad when they ran KCC, Reform is far worse, more disorganised, more inexperienced, and more reckless,” the Liberal Democrat councillor said.
