It is the first competitive meeting between the two sides since 2018, with the visitors now plying their trade in the second tier of Scottish football.
Match preview
Celtic are well on course to make it two-straight Scottish Premiership titles under the helm of Ange Postecoglou, currently nine points clear of Rangers at the top of the league table.
However, the one domestic trophy that Postecoglou could not get his hands on last season was the Scottish Cup, with Rangers ending up the eventual winners, a record that he will want to put straight this season.
The Hoops are undefeated in their last 16 domestic matches, a run stretching back to a 2-0 away defeat against St Mirren in the middle of September, while their home form has been even more formidable.
In the 10 home league matches that Celtic have played this season, they have won all of them, scoring 30 goals in the process, cruising to a 2-0 win against Kilmarnock at Parkhead in their last match in the Scottish Premiership.
Postecoglou's side are competing on all fronts, with the Australian looking to do the treble, and his side again emerged victorious against Kilmarnock last weekend, 2-0 winners at Hampden to set up a final against Rangers in late February.
Greenock Morton will know just how difficult a task awaits them in the fourth round, after cruising through to this stage of the competition by defeating Queen of the South 4-1 in the last round.
After being promoted to the Scottish Championship last season, Morton have fared very well, still finding themselves in contention for promotion, given that they are just six points off the playoff place.
Dougie Imrie's side went on a remarkable run from the beginning of October until December, going undefeated over a 10-game period, winning seven and drawing three of their games in all competitions.
However, the Ton have recently been brought back down to earth, and they have not won in their last five matches, which does not bode well going into a game against the reigning Scottish Premiership champions.
To make matter worse, Morton lost their last match against Hamilton, the team that are currently four points adrift at the bottom of the league table, and they will know that only a massively improved performance will give them any hope of qualification on Saturday.
Celtic form (all competitions):
W
W
W
D
W
W
Greenock Morton form (all competitions):
W
D
L
D
L
L
Team News
Given that they are coming up against lower-league opposition, Celtic may make a few changes to the team that ran out 4-0 winners against St Mirren in the week.
Scott Bain could be handed a rare start between the sticks, with Tomoki Iwata making his first appearance for the club just in front of him, partnering compatriot Yuki Kobayashi in the centre of defence.
Elsewhere, Matt O'Riley could be given a rest in central midfield, with Aaron Mooy coming in, playing alongside Callum McGregor and Reo Hatate, with James Forrest and Daizen Maeda supporting Kyogo Furuhashi in attack.
Robbie Muirhead is Morton's top scorer this season, netting on seven occasions in 20 appearances, and the 26-year-old is poised to lead the line again, in a 4-2-3-1 system.
Jack Baird and Efetobore Ambrose have been the consistent centre-back pairing for the Ton this season, and they will face the difficult task of keeping Celtic quiet on Saturday.
Celtic possible starting lineup:
Bain; Ralston, Kobayashi, Iwata, Johnston; Mooy, Hatate, McGregor; Maeda, Forrest, Furuhashi
Greenock Morton possible starting lineup:
Schwake; Grimshaw, Baird, Ambrose, Strapp; Blues, McGrattan, Roy, Crawford, Miller; Muirhead
We say: Celtic 5-0 Greenock Morton
In truth, it should be a complete mismatch, with 52-time Scottish champions Celtic the vastly superior team, especially considering how well they are doing in the league this season.
As such, it is not likely to be a matter of whether Celtic win, rather how many they win by, and we expect them to cruise home to a very comfortable victory.