The 25-year-old moved to Elland Road on loan from RB Leipzig in January 2020 and the Whites agreed an obligation to buy the Frenchman for €21m (£18m) if they secured promotion to the Premier League.
However, Augustin played for just 48 minutes across three appearances for Leeds, who won the 2019-20 Championship title under Marcelo Bielsa, and the striker has been battling a legal dispute with the West Yorkshire club ever since.
Leeds believe they were not entitled to sign Augustin on a permanent basis as his loan expired on June 30, 18 days before their promotion from the Championship was confirmed during a Coronavirus-hit campaign.
However, The Athletic reports that Leeds are required to pay Augustin £24.5m in compensation after their former striker took his case against the club to the FIFA's Dispute Resolution Chamber, who 'found partially in his favour'.
The report adds that Leeds have appealed against the decision and a spokesperson of the Premier League outfit has revealed that "the club cannot comment on an ongoing legal matter."
Augustin is said to be receiving the full payment of his initially agreed five-year contract with Leeds believed to be worth between £80,000 and £90,000 per week.
Leeds lost an initial appeal over the case with the Court of Arbitration for Sport (CAS) in November last year before reaching an agreement with Leipzig to pay a £15.5m settlement.
However, the case was officially closed following an "amicable resolution of the dispute between the clubs".
The latest appeal from Leeds will result in another hearing with CAS and it remains to be seen when that will take place.
After leaving Elland Road at the end of the 2019-20 season, Augustin left Leipzig to join French side Nantes on a free transfer, penning a two-year deal.
However, Augustin battled with Long Covid during his first season at the club and was reduced to just three appearances before featuring only seven times as a substitute the following campaign.
The striker then made the switch to Swiss giants Basel on a free transfer last summer, signing a three-year contract, and has scored four goals in 18 games during an injury-hit 2022-23 season.
Augustin has contributed with one goal and one assist in his last two league appearances for Basel, who are currently languishing in sixth place in the Swiss Super League table, five points behind the Champions League positions and 22 points adrift of Young Boys at the summit.
Leeds, meanwhile, remain in danger of relegation from the Premier League as they sit 16th in the table, just two points above the bottom three with eight matches remaining.