McGeeney, Armagh's 2002 All-Ireland winning captain, brought Kildare to an All-Ireland semi-final in 2010 but his tenure ended in controversial circumstances in 2013 after losing a ballot by county delegates by one vote.
Kildare will be without impressive midfielder Kevin Feely after he picked up his third black card of the year against Dublin yesterday and captain Eoin Doyle looks set to have a procedure performed on a broken thumb.
No beaten Leinster finallist has gone on to win their Round 4 qualifier since the Lilywhites did it in 2009.
Monaghan suffered a shock Ulster semi-final defeat to Down in their Ulster semi-final but have come through qualifiers against Wexford and Carlow and will relish the chance to gain some revenge.
The winners if these games will play either Dublin or Tyrone. If Kildare win they will face Tyrone in the last eight. If Armagh and Monaghan win, then another draw will be required next Monday.
Both matches will be contested on the weekend of 29-30 July, with venues, times and dates to be confirmed by the Central Competitions Control Committee (CCCC) on Monday afternoon.