Giovanni Trapattoni’s men finished runners up to Russia in Group B after a 2-1 win over Armenia at the Aviva Stadium on Tuesday night.
They will now face back-to-back games against another second placed European nation in November to see whether they will participate in the finals.
However, their chances of making the tournament in Poland and Ukraine have received a boost, as the Emerald Isle will avoid Portugal, Czech Republic and Croatia, who have all been seeded ahead of the draw.
This means that the celtic nation will have to beat Montenegro, Estonia, Bosnia-Herzegovina or Turkey over two legs if they are to make the European Championships.
The first leg of the tie will be played on either November 11th or 12th, with the decisive second leg on November 15th.
All playoff teams will be looking to join the likes of Poland, Ukraine, England, Spain, Germany, Russia, Italy, France, Holland, Greece, Denmark and Sweden, who are all already assured a place in the competition.
By Gareth McKnight