Hearts and Partick Thistle have described a letter received by clubs from the SPFL relating to the pair's court action as "wrong" and "misleading".
The clubs are challenging their demotions, as well as the promotions of Dundee United, Raith Rovers and Cove Rangers.
The hearing will take place via video conference from 11:00 BST on July 1.
The SPFL made no comment when asked for a response by BBC Scotland.
"Along with the other 40 SPFL clubs, Hearts and Partick Thistle have received a letter, signed by [SPFL chief executive] Neil Doncaster, that relates to the forthcoming court case," the joint statement said.
"It is wrong and much of its content is misleading and the timing itself questionable, we are currently awaiting legal advice on what needs to happen next."
Hearts and Thistle are challenging their respective relegations from the Premiership and Championship after clubs voted to curtail the season.
United, Raith and Cove were declared winners of the Championship, League One and League Two and the petition asked for a judge to scrap promotion and relegation for the 2019-20 season.
The action came after SPFL clubs failed to support the league's proposal for reconstruction, which would have kept Hearts, Thistle and League One's bottom side Stranraer up.