Ireland are searching for a new manager following the departure of Giovanni Trapattoni on Wednesday after five years at the helm.
Football Association of Ireland chief executive John Delaney has revealed that McDermott was one of the names under consideration to succeed Trapattoni.
McDermott, who took charge at Elland Road in April, admits he would love to manage the Republic of Ireland at some point in the future, but that he has no plans to leave Leeds.
"One day I want to manage Republic of Ireland. But I'm at a fantastic club," said McDermott.
"I owe them and the supporters. I'm committed 100 per cent."