After Saturday's action, Clare, Laois, Mayo and Tyrone have emerged to take on one of the provincial runners-up next weekend.
Cork will be in one pot along with Galway, Cavan and Meath. The only repeat pairing which won't be permitted is Laois against Meath.
Tyrone are the team to avoid after they blitzed Kildare in Newbridge, 2-22 to 1-15, serious shooting, while Mayo are the other high-profile county left in the mix after holding on in a thriller against Armagh.
James Horan's charges got 1-1 from sub Kevin McLaughlin while Cillian O'Connor made his return from the bench to nail two pressure frees. However, Lee Keegan hobbled off to add to the county's injury woes.
Clare were 1-13 to 0-15 victors away to Westmeath, with David Tubridy hitting the net and Gary Brennan coming up with some major plays in the closing stages. The hosts did lose key players Ger Egan and John Heslin in the first half.
Cork would be delighted to draw the Banner when the pairings are revealed on Monday morning but the feeling is mutual, especially after Clare's resounding win in the league this spring, which had a major bearing on Ronan McCarthy's side dropping down to Division 3.
Laois were 0-20 to 0-15 winners over Offaly.