The draw for Round 4B of the qualifiers was made on Monday morning and gives Monaghan the chance to avenge their Ulster semi-final defeat to the Mournemen.
Both games will also be shown live on Sky Sports with Armagh's game throwing in at 7pm.
They went on to lose Sunday's Ulster final to Tyrone, with Mickey Harte's side running out comfortable 2-17 to 0-15 winners in Clones.
Undoubtedly the pick of the two ties is Kildare vs Armagh, as Kieran McGeeney faces off against his former county.
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For a full list of this weekend's fixtures and upcoming fixtures, visit the official GAA's fixtures and results page.
No beaten Leinster finalist has gone on to win their Round 4 qualifier since the Lilywhites did it in 2009. Should Kildare win they will automatically play Tyrone, while should Down win they will automatically face Dublin.
The games will be played at neutral venues on Saturday 29 July, which will be confirmed later today by the CCCC. If Armagh and Monaghan win, then another draw will be required next Monday.