The Blades are claiming £30million in damages for being relegated from the Premier League after winning an arbitration tribunal ruling last month.
West Ham are due to submit a claim to the Court of Arbitration for Sport (CAS) in Lausanne on Thursday, asking them to rule on the case, and are also considering High Court action.
If Sheffield United do not give the go-ahead for CAS to arbitrate in the case, however - and there has been no sign of that so far - then that hugely decreases the chances of that court agreeing to take the case.
A West Ham spokesman called on the Blades to agree to take the case to CAS.
The spokesman said: "We do believe that the arbitration panel's ruling needs to be reviewed by a court which can help resolve the outstanding issues in this case.
"This is not about the issue of damages - the current ruling has major implications for English football.
"West Ham will continue to look at the available options for further action and we do believe that Sheffield United should join us in a hearing at the Court of Arbitration."