Monaghan will start their defence of the Ulster Football Championship with a quarter-final meeting against Down.
Malachy O'Rourke's men won the provincial crown for the second time in three years by beating Donegal in the 2015 final.
Down lost to Derry last year and boss Jim McCorry quit after just one season.
Derry have been drawn against Tyrone while Cavan meet Armagh and Donegal face the winners of the preliminary round tie between Fermanagh and Antrim.
Ulster Football Championship 2016
Fermanagh v Antrim
Donegal v Fermanagh or Antrim
Derry v Tyrone
Cavan v Armagh
Monaghan v Down
Leinster Football Championship 2016
Laois v Wicklow
Louth v Carlow
Longford v Offaly
Laois or Wicklow v Dublin
Louth or Carlow v Meath
Longford or Offaly v Westmeath
Wexford v Kildare
Connacht Football Championship 2016
Roscommon v New York
Roscommon or New York v Leitrim
Roscommon/New York/Leitrim v Sligo
Mayo or London v Galway
Munster Football Championship 2016 quarter-finals
Tipperary v Waterford
Clare v Limerick
Clare or Limerick v Kerry
Tipperary or Waterford v Cork