A win over England tomorrow would put Ireland on top of the World Rankings for the first time ever.
Last week, Wales defeated Eddie Jones' men to leapfrog New Zealand into the top spot for the first time in their history.
But with the top two taking a week off, Ireland could jump into the number one spot with victory in their World Cup warm-up fixture at Twickenham.
If fifth-ranked England win by more than 15 points, however, they would knock Ireland down to fourth place.
The All Blacks had held the top spot for close to a decade, from November 2009 until last week.
The rankings began in September 2003, with England and South Africa the other two countries to have topped the list.