Lawyers for two former politicians will replace Mcclory as Minister of Law Office Logo.
Sources say the two former MPs are expected to be confirmed by the Government.
The decision comes after the Government was forced to cancel an earlier announcement that Mccluskey would become the new Minister of State for Justice and Attorney-General.
It was understood that the Cabinet decided to remove Mccloskeys appointment from the agenda due to a lack of support for the position.
Sources have told RTE the new role is being considered by the Attorney-Genial Council, which is responsible for appointing new ministers.
The Cabinet is also expected to make a final decision on the appointment of a new Minister for Health and Social Care in the coming days.
The Government was expected to announce the appointment on Friday.
The new Minister will be chosen in the next Cabinet reshuffle, which will see the Cabinet reshuffled in the following days.
Source: RTÉ News