Rangers face playing their William Hill Scottish Cup clash at Tannadice with a much-diminished away backing after one of their main supporters groups called for an organised boycott.
Rangers were paired with Dundee United in the fifth round, the first occasion they have been drawn away against Clydesdale Bank Premier League opposition since they were relaunched as a new company and denied entry to the SPL. The Rangers Supporters Assembly urged fans to participate in a "full boycott".
A statement from the group read: "The Rangers support has waited patiently for the opportunity to send a clear message to those that tried to destroy our club - starve them of their much-needed cash by boycotting this game."
The statement continued: "It must also be remembered the disregard this club had for Rangers supporters when it unashamedly refused to offer refunds to supporters for a game abandoned due to a waterlogged pitch in 2009.
"We also understand the desire to support the team - the fans have demonstrated this to unbelievable lengths of loyalty - but we ask that on this occasion in a one-off display of fan power we show that we have not been beaten or broken."
Celtic will also face old cup foes in the form of Raith Rovers, who beat them in the 1994-95 League Cup final, should they get past Arbroath in a replay.
Raith midfielder Simon Mensing, who played in a 4-1 Parkhead defeat in the League Cup in September, said: "If Celtic were to progress it's massive for the club. It's a home game too. We put on a decent performance at Parkhead so hopefully we can take the positives out of that."
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. They face the winners of the rearranged clash between Cowdenbeath and St Johnstone, which was due to be played on Tuesday night but has been postponed for a second time.
Dundee are at home against 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. The ties will be played on the weekend of February 2 and 3.