Kotoko reached seven African Champions League finals between 1967 and 1993, but won just two, and also finished runners-up in their sole African Cup Winners Cup final appearance three years ago.
At the core of the dispute is the Deed of Gift, a 1, 200-word legal document penned in 1887 by George Schuyler, then the sole surviving member of the syndicate that first won the Cup.
With a potential May date with Argentina hanging in the balance, South Africa's sole confirmed friendly in the run-up to the World Cup is a 5 June meeting with Denmark.