Irish Justice Minister Dermot Ahern wrote to Northern Ireland's minister for social development Margaret Ritchie to discuss a country-wide venture to end volume-based offers.
He wrote: "I am conscious that the effectiveness of
to curb such promotions could be reduced if
action is not taken on an island-wide basis."
The Republic of Ireland has already outlawed BOGOF deals and reduced the times when alcohol can be sold.
But in an emergency Budget last month, Eire decided not to hike drinks taxes
amid fears that a price increase would drive more people to buy cheaper alcohol in Northern Ireland.
Ahern said in his letter: "I would welcome an opportunity to discuss the possibility of a joint
north- south initiative to tackle alcohol promotions, especially the volume-based promotions which
are designed to increase the quantities sold and which, in some cases at least, result in excessive consumption of alcohol and various types of alcohol-related harm."