The Irish FA will maintain John O'Shea as caretaker head coach in the summer.
Georgia manager Willy Sagnol is being linked to the post, as he may be free after Euro 2024, says The Sun.
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O'Shea took over on a temporary basis in February after Stephen Kenny's departure.
He managed the team for a 0-0 against Belgium and a 1-0 loss to Switzerland.
Ireland are not in Euro 2024, as they failed to qualify under manager Kenny in 2023.