More than 40,000 Asda store workers, about two-thirds of whom are women, have brought equal pay claims after complaining that staff working in distribution depots unfairly get more money.
Asda bosses say store jobs are not comparable to distribution centre jobs.
Store workers, who are represented by law firm Leigh Day, have made sex-discrimination claims.
They say store workers have historically got less because most store workers are women, and most distribution depot staff are men.
Lawyers representing store workers say distribution depot workers get between £1.50 and £3.00 an hour more.
Supreme Court justices were asked to consider whether Asda store workers are entitled to compare themselves to distribution staff for equal pay purposes.
Judges considered arguments at a hearing in July and are due to deliver a ruling on Friday.
Lawyers say the ruling will have implications for supermarkets, and other retailers.
The litigation began some years ago.
In 2016, an employment tribunal decided that store workers were entitled to compare themselves to distribution staff.
That decision was upheld by Court of Appeal judges in 2019. Asda bosses then appealed to the Supreme Court.
Lawyers say the store workers’ fight will not end, even if Supreme Court justices rule in their favour, and the litigation could run on for years.
They say the next stage would involve an employment tribunal deciding whether specific store and distribution jobs were of “equal value”.
If judges decided that different jobs were of “equal value”, the litigation would then enter a third stage.
Lawyers say an employment tribunal would then consider whether there were reasons – other than gender – why people working in stores should not get the same pay rates as people working in distribution centres.
Store workers bringing claims are members of the GMB union.