Steven Gerrard's men have once again progressed from the first round of the Europa League qualifiers, while the Parkhead side have dropped from the Champions League at the penultimate hurdle.
Celtic are tasked with seeing off Swedish champions AIK, who are currently second in the Allsvenskan, while Rangers are required to get past Polish giants Legia Warsaw - runners up last campaign but off to a slow start this season.
Reach the group stages of Europe's secondary competition and they will be required to play a number of games on the Sunday.
Europa League fixtures take place on the following days:
19 September 2019
3 October 2019
24 October 2019
7 November 2019
28 November 2019
12 December 2019
It means that six Rangers matches, scheduled for Saturday, will have to be moved, while Celtic will see four games shifted as they are already due to travel to Livingston and Aberdeen away on the Sunday following matchday 2 and 3 of the competition.
However, there will be no Betfred Cup farce as happened last season when both semi-finals had to be played on the Sunday due to the Old Firm's participation in the Europa League.
Celtic fixtures to be moved (scheduled date in brackets):
Kilmarnock H (21 September)
Motherwell H (9 November)
Ross County A (30 November)
Hibernian H (14 December)
Rangers fixtures to be moved (scheduled date in brackets):
St Johnstone A (21 September)
Hamilton Academical H (5 October)
Motherwell H (26 October)
Livingston A (9 November)
Heart of Midlothian H (30 November)
Motherwell A (14 December)