Donegal will face Kildare in the All-Ireland Football quarter-finals while Tyrone will meet Dublin if the Red Hands beat Roscommon next weekend.
Kildare impressively defeated Derry on Saturday and Jim McGuinness' Donegal side will face a difficult task against Kieran McGeeney's Lilywhites.
Tyrone also have a tough tie in prospect against a Dublin side that beat them at the stage stage last year.
In the other last-eight games, Kerry face Limerick with Cork taking on Mayo.
The winners of the Kerry-Limerick clash will then go on to face either All-Ireland champions Cork or Mayo in the semi-finals.
Donegal or Kildare will meet either Dublin, Tyrone or Roscommon in the other All-Ireland semi-final.
The dates and times for the quarter-finals are expected to be announced on Monday.
Kerry and Cork appear to have landed the more favourable draws.
The Kingdom will face a Limerick side that earned a hugely controversial 1-18 to 1-17 win over Wexford on Saturday evening.
Wexford led by three points going into injury-time but Limerick then levelled with a goal and took the victory with an Ian Ryan free which one umpire waved wide.
Referee Derek Fahy consulted with the other umpire before deciding to award the score - much to the consternation of the Wexford players, management and fans.
Wexford goalkeeper Anthony Masterson insisted that Ryan's free "looked like it was a yard wide".
But despite the controversy, Limerick were in Sunday evening's quarter-final draw.
In the hurling semi-finals, Waterford, after their 2-23 to 2-13 win over Galway on Sunday, will take on Kilkenny on 7 August with Tipperary facing Dublin a week later.
Dublin defeated Limerick 3-13 to 0-18 on Sunday.
All-Ireland SFC quarter-finals
Kerry v Limerick
Mayo v Cork
Donegal v Kildare
Dublin v Tyrone/Roscommon