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:
Laois Can Improve Plenty - Enda Lyons
Laois fought back from an eight point deficit against Offaly last weekend.
Top Six Chasing Athlone Welcome Cobh To Westmeath
Town are looking for a fourth win in five games.
Westmeath Staring Down The Barrell For Midlands Derby
Midlands 103 analyst Gerry Buckley looks forward to a crunch clash in Tullamore.
Offaly's Minor Football Campaign Ends Meekly In Aughrim
The Faithful County fell behind early and never got back on terms.
Aoife O'Rourke Fighting For Silver Today
The Ballinasloe fighter faces a Turkish opponent in Belgrade.
"You Have To Look At The Things You Can Control" - Lee Pearson
The Offaly captain previews the Faithful's meeting with Dublin.
Turner Wins Another Major Championship Medal
The Portarlington swimmer landed bronze in Belgrade on Tuesday evening.
Henshaw Still Supporting Buccaneers
Henshaw's former club have had a tough season in AIL action.
Aoife O'Rourke Wins Another European Medal
There was less fortune for Aoife's sister Lisa in Belgrade yesterday.
Westmeath U20s Clinch Final Spot
A strong win over Carlow sees the Lake County progress in the Andrew Corden Cup.
Offaly Rider Dominates Mondello Masters Opening Rounds
Edenderry's Kevin Keyes hit a hat-trick in the Superbike category.
Westmeath Under 20s Face Tough Test To Progress To Final
There's also a midlands derby this weekend in the Leinster Minor Hurling Championship.
Westmeath Struggles Are A Credit To Kerry - Tommy Doyle
The Lough Lene Gaels man reflects on a disappointing performance by Westmeath.
Nicole Turner Taking On Best Of Europe In Madeira
Roisin Ni Riain has already won two medals for Ireland at the championships.
O'Rourke Sisters Fighting For More Major Medals Today
The Ballinasloe sisters are fighting for European bronze medals today.
Words Fail Me - Offaly Manager Left Shocked At Loss To Laois
Johnny Kelly's side were in control of their championship opener for the first 50 minutes.
Westmeath Fight Back To Secure Championship Opening Draw Against Offaly
Westmeath recovered from a strong Offaly start in Mullingar to retrieve a draw.
I Want The Blame To Fall On Me - Joe Fortune
The Westmeath manager is reacting after his side suffered a costly defeat.
Goal Of The Season Contender Secures Athlone First Away Win
Carl Mujaguzi's volley won Athlone three points in Tralee on Friday.
Laois Enjoy Sun Kissed Comeback Victory Over Offaly
Willie Maher's men looked out of the contest midway through only to come roaring back.
