The deal, which allows a company in the Sports Direct group to sell replica Rangers kit and other branded products, is expiring.
Bosses at Rangers want to sign a new deal with a third party.
SDI Retail Services bosses object and say they should have a chance to match any new offer.
A judge on Wednesday said he would analyse evidence about the meaning of a contract clause at a High Court trial in London in late July.
Mr Justice Phillips said bosses at Rangers should not sign any new deal until he had ruled on the
The judge heard arguments about the dispute, from lawyers representing both sides, at a preliminary hearing in London on Tuesday.