The Hammers issued a statement which read: "We are extremely disappointed that Sheffield United have seen fit to embark on this latest desperate action.
"Not only does Sheffield United's claim lack legal merit, but it is also based on their incorrect belief that West Ham withheld an agreement from the Premier League and the April disciplinary commission.
"In fact, long before the disciplinary hearing, West Ham United made the Premier League fully aware of the existence and status of the agreement in question.
"This agreement was then included in the documentation produced for the disciplinary commission, who were therefore also aware of its existence throughout the proceedings.
"Sheffield United's latest assertions clearly demonstrate a fundamental misunderstanding of the situation, and any proceedings brought by them will be vigorously defended by West Ham.
"In the meantime, West Ham and the new owners will not permit these repeated slurs to go unchallenged and are in discussions with their legal advisers in relation to the action they might take."
"Sheffield United will claim substantial damages for breaches of contract by West Ham.
"Sheffield United's basis for the claim is that West Ham acted dishonestly in obtaining the registration of Carlos Tevez and Javier Mascherano, in that they failed to reveal that those players were owned by a third party.
"The Premier League would not have registered those players with West Ham had they known the true position.
"The players, particularly Tevez, played a key role in West Ham's season, giving West Ham an unfair advantage at the expense of the other Premiership teams - including Sheffield United - all of which had played by the rules.
"Sheffield United are confident that sufficient remedies exist in law to ensure the Tevez affair cannot simply be brushed under the carpet."
The Blades have put the cost of relegation at between £30million and £50million.