The Jam Tarts claimed their place in the last 16 with a 1-0 win over Aberdeen at Tynecastle on Saturday evening while the Hibees defeated Championship rivals Raith Rovers 2-0 in Kirkcaldy.
The match will almost certainly be moved for live television and, with Scotland due to host England in their Six Nations opener at BT Murrayfield on the Saturday, the derby is likely to be put back 24 hours.
East of Scotland League champions Lothian Thistle Hutchison Vale, meanwhile, will have a dream home tie against Premiership champions Celtic should they overcome East Kilbride in their fourth-round clash, which was postponed due to snow at the weekend.
Junior outfit Linlithgow Rose, who face a replay with Forfar Athletic tomorrow week following Saturday’s 3-3 draw at Prestonfield, will take on either Dunfermline or Ross County in the last 16 should they progress.
Rangers were handed a home clash against Kilmarnock.
Motherwell v Striling Albion/Inverness Caley Thistle; East Kilbride/Lothian Thistle v Celtic; Dundee United v Partick Thistle; Dunfermline/Ross County v Linlithgow Rose/Forfar Athletic; Rangers v Kilmarnock; Annan Athletic v Greenock Morton; Dumbarton v Dundee/Falkirk; Hearts v Hibs. (Ties will be played on the weekend of February 6-7).