The Italian's contract expires next year and, with the Green Army's hopes of qualifying for the World Cup hanging by a thread, a new deal is unlikely to be tabled.
Speculation regarding his future has been the subject of debate since a disappointing Euro 2012 campaign in which they were eliminated without scoring a goal.
According to the Daily Mail, the Football Association of Ireland will turn to the former Sunderland and Aston Villa boss before embarking on the path to qualify for the 2016 European Championships in France.
The 61-year-old from Kilrea, Northern Ireland, has been without a job since being sacked by the Black Cats in March.
Ireland are currently fourth in their World Cup qualifying group, three points behind second-placed Sweden and level with Austria.