The Hoops are seeking their third consecutive triumph in the competition but their recent Easter Road record isn't the best.
Scottish Cup holders Celtic have been drawn away to Hibernian in the quarter finals of this season's competition.
Brendan Rodgers's charges sealed their place in the last eight after running out 5-0 winners over St Johnstone in the fifth round on Sunday - their 24th win in a row in domestic cups.
Their reward is a trip to Edinburgh to face the Scottish Premiership's eighth-placed side, who Celtic beat 2-0 at Parkhead in the league just last week thanks to goals from Ryan Christie and Oliver Burke.
Hibs, meanwhile, beat Raith Rovers 3-1 in the fifth round and will be hoping to deny the Hoops the opportunity for a third consecutive Scottish Cup, and they could well fancy their chances given their good recent record against them at Easter Road.
Celtic's last three trips to Leith have yielded two defeats and a draw (Soccerbase), so after the draw was made and announced by Celtic's Twitter page, some Hoops fans seemed concerned despite their overall good record in cup competitions:
Restart the draw that was just a practice— Marcus (@MarcusT1402) February 11, 2019
Hopefully put a performance in unlike have done for a while in Edinburgh— Sean Fleming (@SeanFleming1916) February 11, 2019
Oh— james kerrigan (@jtkerrigan_) February 11, 2019
Announce out in the quarters— Keir Orr (@OrrKeir) February 11, 2019
Some fans, meanwhile, were a little more optimistic, considering Hibs have struggled recently:
Bring it on. Lots of new faces in the squad & long term ones who have stepped it up recently & probably have a couple more gears to go up— Kevin Barry (@Kevin_Barry) February 11, 2019
4 nil for the bhoys another treble on the way— StevieShroom☮️UTLR (@stevieshroom) February 11, 2019
Good draw on current issues at hibs— john macphee (@cfc96317967) February 11, 2019
Edinburgh record is worrying but we’re playing a hibs side that showed no fight the other week without Lennon, need to go to places like this and win if we’re going for— anthony mackenzie (@tony__mackenzie) February 11, 2019
The last-eight ties will take place around the weekend of March 2-3.