A former Minister, who lost his position during the Golf-gate controversy, is earmarked for the role.
Longford Westmeath TD Robert Troy's Junior Ministry is likely to be filled this week.
Senior figures in Fianna Fáil expect a new appointment will be approved by Cabinet on Wednesday, during it's first meeting back since the summer break.
Among those who are being earmarked for the job, include Dara Calleary, who lost the Agriculture Ministry in 2020 during the Golf-gate controversy.
But the Irish Times reports no final decision on the post been made yet.
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