Sheffield United should discover on Tuesday whether their fight to avoid relegation from the Premier League has been successful.
A three-man arbitration panel will finish hearing a challenge brought by the Blades against the Premier League.
Sheffield United plc chairman Kevin McCabe said after giving evidence to the panel: 'I think the panel recognise all the points of the case.
'It's about righting the wrongs from the first decision. That's really part of the arbitration proceedings and why we served the notice on the Premier League back in mid-May.'
The Blades want the panel to order a fresh disciplinary hearing against West Ham over the Carlos Tevez affair.
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 last August, contrary to Premier League rules.
The three-man panel's main role is to see whether the correct disciplinary procedures were followed.
Retired High Court judge Sir Philip Otton is chairing the arbitration tribunal hearing, which is expected to conclude today, alongside David Pannick QC representing the Blades and leading barrister Nicholas Randall.
A statement released on behalf of the panel read: 'Sheffield United are asking the arbitral panel to determine two matters.
'The first is whether the decision by the independent disciplinary commission on April 27 to fine West Ham, rather than dock points, was legally flawed such as to require the issue to be determined afresh by a disciplinary commission at some point in the future.
'The second is whether the Premier League acted unlawfully by not de-registering Tevez. Fulham are seeking similar relief.
'The arbitral panel have no power to decide what the penalty to be imposed upon West Ham should be.'
