It's a repeat of last November's meeting at the same stage.
Offaly will renew rivalries with neighbours Kildare in the Leinster Football Championship Quarter-Finals next Sunday.
It's been confirmed as a 4:30 throw-in in Portlaoise.
John Maughan's side will be looking to avenge a four point loss at the same stage in November.
Speaking after their extra-time win against Louth, Rhode's Niall McNamee says the should have advanced in 70 minutes: