Down to face Mayo on Saturday with Donegal-Kerry on Sunday
Down's All-Ireland SFC quarter-final with Mayo will be played at Croke Park next Saturday with Donegal meeting Kerry a day later at GAA headquarters.
The Down-Mayo clash will start at 17:00 BST with Dublin's game with Laois following at 19:00.
On Sunday, Cork's contest with Kildare will throw-in at 14:00 with the Kerry-Donegal game starting at 16:00.
Donegal's clash with last year's beaten All-Ireland finalists will be the stand-out game of the weekend.
Jim McGuinness' Donegal side produced a hugely impressive Ulster Final dismissal of Down but they will face a massive task against the Kingdom.
Down, after their win over Tipperary on Saturday, will feel they are capable of beating the Connacht champions.
In the semi-finals, the winners of the Donegal v Kerry clash with face either Cork or Kildare with Mayo or Down meeting either All-Ireland champions Dublin or Laois in the other last-four encounter.
Donegal's quarter-final clash with the Kingdom will be the first ever Championship meeting between the counties.
In their most recent meeting in March, Kerry earned a 2-6 to 1-8 win but Donegal have improved significantly since their stuttering start to this season's Football League.
However, last year's beaten All-Ireland finalists also look to be right back in form after losing to Cork in the Munster Championship.
The Kingdom struggled to earn a one-point win over Westmeath in the second round of the qualifiers but then regrouped to produce a huge performance as they beat Tyrone by 10 points in Killarney.
Donegal only managed to sneak past Tyrone by two points in the Ulster semi-final.
On Saturday, Kerry eased into the All-Ireland quarter-finals with a 2-21 to 1-6 win over Clare.
Paul Galvin was sent off in that game but, while there was some confusion after the match, he is understood to have received two yellow cards and should be available for the quarter-final.
Down will not underestimate Mayo but James McCartan will surely be happy to have avoided a clash with either Cork or Dublin.
All-Ireland Football Championship quarter-finals
Mayo v Down [Croke Park, 17:00]
Dublin v Laois [Croke Park, 19:00]
Cork v Kildare [Croke Park, 14:00]
Donegal v Kerry [Croke Park, 16:00]
Cork or Kildare v Donegal or Kerry [26 August]
Dublin or Laois v Mayo or Down [2 September]
All-Ireland Minor Football quarter-finals
Tipperary v Mayo [Croke Park, 15:00]
Roscommon v Kerry [Croke Park, 12:00]
Dublin v Monaghan [Newry, 17:30]
Tyrone v Meath [Newry, 19:15]
WEEKEND GAA RESULTS
All-Ireland Fourth-round Football Qualifiers
Laois 1-15 1-12 Meath
Down 1-13 0-11 Tipperary
Sligo 0-4 0-13 Kildare
Clare 1-6 2-21 Kerry
All-Ireland Hurling Quarter-Finals
Kilkenny 4-16 1-16 Limerick
Cork 1-19 0-19 Waterford