The Blades want the panel to order a fresh disciplinary hearing against West Ham over the Carlos Tevez affair.
Parry was the first chief executive of the Premier League and he was called as a witness by Sheffield United to answer questions about when the rules were first established.
The Blades are claiming that West Ham should have been docked points by an independent commission for including third-party agreements when they signed Tevez and Javier Mascherano, contrary to Premier League rules.
Parry, incidentally, first drew attention to the rule breaches when Liverpool signed Mascherano from West Ham in the January transfer window.
Sheffield United plc chairman Kevin McCabe also appeared as a witness, with Premier League chief executive Richard Scudamore and general secretary Mike Foster appearing for the other side.
The panel can order a new disciplinary hearing against West Ham, or that some compensation be paid to Sheffield United.
The three-man panel's main role is to see whether the correct disciplinary procedures were followed.