Former leader Nick Paget-Brown resigned on 30 June following continued criticism of the council's handling of the Grenfell Tower tragedy.
Local politicians have warned that the new leader must come from outside the "contaminated" administration.
Councillor Daniel Moylan said the ruling Conservative group has to "show a complete break with the past".
Mr Moyland, the Conservative former deputy leader of Kensington and Chelsea Council, said "any idea of a continuity candidate would be a very bad idea".
"We have to be able to go to the people of North Kensington and to the victims of the fire with a real sense of acknowledging how badly they have been let down, a real sense of shame if you like," he told BBC London Radio.
Kensington and Chelsea Conservatives will hold a regular group meeting on Monday evening.
It is expected during this meeting they will vote on replacements for Mr Paget-Brown and former deputy council leader Rock Feilding-Mellen, who also resigned.
The chosen candidates must then gain approval by a vote in full council, a formality given the Conservative group control 40 out of 50 seats on Kensington and Chelsea Council.
Judith Blakeman, a Labour councillor in the ward which houses Grenfell Tower, said "it can't possibly be one of the cabinet members" as they had voted to endorse the former leadership.
"They are all contaminated. No member of the current cabinet would have any credibility with the residents of North Kensington," she added.
Sadiq Khan has called for commissioners to take over the running of Kensington and Chelsea Council.
The Mayor of London said the government had "no option" but to appoint "untainted" commissioners.
The new leader of Kensington and Chelsea Council will be announced later, the BBC understands.