The three-man arbitration panel who have been hearing the Blades' claim are due to announce their verdict some time in the afternoon.
The panel cannot order the League to deduct points from the Hammers but they do have the power to order a fresh independent disciplinary commission look at the case.
Such a ruling, or one saying Sheffield United may have a claim for compensation, would throw the league into disarray because it would be impossible for a new disciplinary hearing and any subsequent appeals to take place before the start of the new season.
The Premier League maintain they handled the whole affair completely by the rule book.
They have consistently argued that the independent commission's original decision to fine West Ham rather than dock points should not be overturned simply because another club do not agree with it.
West Ham breached Premier League regulations by including third-party agreements when they signed Tevez and Javier Mascherano last summer. As a punishment they were fined £5.5million in April.
The arbitration panel, headed by retired High Court judge Sir Philip Otton, have been charged with determining two matters: whether the decision by an independent disciplinary commission on April 27 to fine West Ham rather than dock points was so legally flawed that a fresh disciplinary commission need to sit, and whether the Premier League acted unlawfully by not de-registering Tevez.
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