Rangers have been drawn away against Dundee United in the fifth round of the William Hill Scottish Cup.
United knocked Gers out of last season's tournament, days before the Ibrox oldco club went into administration.
Celtic face a trip to Raith Rovers, the team that shocked them in the 1994-95 League Cup final, should they get past Arbroath in a fourth-round replay.
Hibernian's reward for their derby win over holders Hearts is another home tie against SPL opposition in the form of Aberdeen or Motherwell, who drew 1-1 at Pittodrie on Saturday.
Another top-flight tie will see Kilmarnock host the winners of the Highland derby replay between Inverness and Ross County.
St Mirren are at home again following their win over Brechin, facing the winners of Tuesday night's rearranged clash between Cowdenbeath and St Johnstone.
Dundee are at home to Turriff United or Morton. The Highland League side held Allan Moore's team to a 1-1 home draw on Saturday.
Dunfermline are at home to the winners of the postponed clash between Dumbarton and Hamilton, while Falkirk will host Forfar.
William Hill Scottish Cup fifth-round draw: Raith v Celtic/Arbroath, St Mirren v Cowdenbeath/St Johnstone, Dunfermline v Dumbarton/Hamilton, Hibernian v Aberdeen/Motherwell, Falkirk v Forfar, Dundee United v Rangers, Dundee v Turriff/Morton, Kilmarnock v Inverness/Ross County.
Ties to be played on the weekend of February 2 and 3, 2013.