Liverpool chief executive Rick Parry has given evidence reportedly backing Sheffield United at an arbitration tribunal as part of the Blades' bid to avoid relegation from the Premier League.
United want the panel to order a fresh disciplinary hearing against West Ham over the Carlos Tevez and Javier Mascherano affair and remain hopeful they will be reinstated to the Premier League.
The panel will rule whether the decision to fine and not dock the Hammers points was the correct course of action.
United's 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.
Asked what he expected from the arbitration panel, McCabe told Sky Sports News on Sunday: "I'd like to believe it will be reinstatement of Sheffield United in the Premier League.
"The first decision was wrong. It should have been points deducted and not a monetary fine.
"West Ham have then to be sorted out by the Premier League - they have their own board and that's their decision.
"If the arbitration goes against us, and we firmly believe it won't, then we have to accept next season we will be in the Championship and we'll prepare for that.
"If we'd have had Carlos Tevez, we'd have won enough football matches.
"That really is the nub of this sad lack of integrity of English football and that's what's got to be sorted out tomorrow and Tuesday."