Armagh will play Meath before Monaghan meet Kildare in a Croke Park double-header of All-Ireland qualifiers round 4B on Saturday, 2 August.
The Orchard team, impressive winners over Roscommon in Saturday's qualifier, take on the defeated Leinster finalists at 17:00 BST.
Monaghan's defeat by Donegal in the Ulster decider leaves them facing a 19:00 clash with the Lilywhites.
The winners will progress to the All-Ireland SFC quarter-finals.
Provincial champions Donegal and Dublin await the round 4B winners in 9 August quarter-finals.
Armagh overcame Ulster rivals Tyrone before beating Roscommon 1-17 to 1-12 while Meath were hammered 3-20 to 1-10 by the All-Ireland champions.
Monaghan lost their Ulster crown at Clones and they will aim to bounce back against a Kildare team which edged out Clare 0-13 to 0-12 in a Cusack Park qualifier on Saturday.