The liquidators of oldco Rangers were granted leave to appeal to the court over a ruling that the use of Employee Benefit Trusts (EBTs) broke tax rules.
Rangers used the scheme from 2001 until 2010 to give millions of pounds of tax-free loans to players and other staff.
HM Revenue and Customs (HMRC) lost two tribunals before judges agreed these were salary payments subject to tax.
The decision was in relation to Murray Group companies, including the liquidated company RFC 2012 - formerly The Rangers Football Club PLC.
It has no impact on the current owners at Ibrox.
However, liquidators BDO were allowed to appeal as the ruling has implications for future cases.
The  Supreme Court judges will deliver their binding verdict, which will be screened live on its website, at 09:45 on 5 July.
A final verdict on the Rangers "big tax case" will be delivered next Wednesday, the Supreme Court has announced.