Giovanni Trapattoni's side, who beat Armenia 2-1 on Tuesday to secure a playoff place, have been seeded in the top half of the draw and will be draw against either Turkey, Bosnia-Herzegovina, Estonia or Montenegro.
When asked which side he wanted to be drawn against, the Aston Villa shotstopper said: "Somebody easy.
"We will just take it on the chin. Whoever we play will know they are in for a very tough game when they come here, and we will give them a tough game at their home place as well.
"Please God, we can get across the line this time and get through the playoffs."
The Republic last took part in a major international tournament at the 2002 World Cup in Japan and South Korea.