International tug-of-war for top Man Utd prospect
Staunton's decision came after Northern Ireland boss Nigel Worthington revealed that he was trying to persuade Gibson to switch allegiance from the Republic.
The 19-year-old, who was born in Londonderry, is currently at the centre of a dispute between the two countries.
Gibson played for Northern Ireland U16s but then opted for the Republic.
Since then, he has earned U17, U19 and U21 caps for the Republic and he was scheduled to be involved in Tuesday's U21 international against Germany in Furth.