The hosts enjoyed a productive trip to Switzerland in midweek which means they are now just two matches away from group-stage football in this season's Champions League.
Match preview
Rangers are potentially 180 minutes away from securing a place alongside arch rivals Celtic in the Champions League group stage after overcoming Swiss outfit Servette in the third qualifying round.
A first-half goal from Dereck Kutesa at Stade de Geneve on Tuesday briefly levelled the two-legged affair following a 2-1 victory for Michael Beale's men last week, however a second-period strike from the always-reliable James Tavernier secured a 3-2 win on aggregate.
The Scottish giants must now conquer Eredivisie challengers PSV Eindhoven for a spot in the group stage of UEFA's elite club competition, however attention turns to the League Cup this weekend.
Having won the competition 27 times since its inception in 1947, Rangers on the most successful club in the League Cup, however it was heartbreak last season as they were defeated 2-1 by Ange Postecoglou's Celtic in the showpiece match at Hampden Park.
The Gers have endured an indifferent start domestically this term, losing away at Kilmarnock on the opening day of the Scottish Premiership season before dispatching Livingston 4-0 at Ibrox a week later.
Greenock Morton have also commenced their respective league campaign with three points from two outings, although the visitors' most recent match ended in defeat last Saturday.
Dougie Imrie took his Morton men to Stark's Park to face Raith Rovers, with strikes from Jack Hamilton, Lewis Vaughan and Callum Smith seeing the Kirkcaldy-based club come out on top of a five-goal thriller.
The 'Ton have been in competitive action since the middle of July due to their participation in the group stage of the League Cup, with Saturday's visitors collecting nine points from a quartet of fixtures to finish only behind Ross County in Group D.
Greenock have been unable to get the better of Rangers in their last five meetings, although many supporters will recall their impressive 2-2 draw against a second-tier Gers side back in December 2015 - a game in which Stefan McCluskey put Morton ahead in.
Saturday will be the first time Imrie's men have featured in the knockout stages on the League Cup since the 2019/20 season, when a penalty-shootout defeat to Hibernian halted their progress in the competition at the round of 16.
Rangers form (all competitions):
L
D
L
W
W
D
Greenock Morton Scottish League Cup form:
W
W
L
W
Greenock Morton form (all competitions):
W
W
L
W
W
L
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Team News
Rangers boss Beale has a glut of injuries to deal with ahead of Saturday's cup clash, one of which being Ridvan Yilmaz, with the six-time Turkey international expected to be sidelined for a few weeks due to a muscle strain.
The Gers are yet to see the return of experienced midfielder Steven Davis following his cruciate ligament injury back in December 2022, although the 38-year-old is aiming to make a comeback later this month.
With a crucial match in the Champions League against PSV fast approaching, expect a raft of changes from the XI who drew with Servette last time out, meaning the likes of Todd Cantwell and Nicolas Raskin should drop to the bench.
Greenock could hand a second debut to 24-year-old Iain Wilson at Ibrox this weekend, after the midfielder's return to the club was announced on Wednesday, making the loan switch from third-tier side Queen of the South.
Robbie Crawford is expected to be in the visitors' XI despite transfer speculation swirling around Morton's talisman - manager Imrie revealed that the club are yet to receive any formal bids for the attacking midfielder.
Rangers possible starting lineup:
McCrorie; Sterling, Balogun, King, Ridvan; Jack, Cifuentes; Dowell, Hagi, Matondo; Danilo
Greenock Morton possible starting lineup:
MacDonald; McGrattan, O'Connor, Broadfoot, Waters; Blues, Crawford, Power; Quitongo, Boyd, Muirhead
We say: Rangers 3-0 Greenock Morton
Rangers are likely to field a second-string side with one eye on their match against PSV on Tuesday, however Beale's men should still possess more than enough to book their place in the quarter-finals.