West Ham were fined £5.5million over irregularities over the signings of Carlos Tevez and Javier Mascherano earlier in the season.
But the courts are likely to be asked to decide whether the London side should be docked points - which could see them make the drop instead.
Chairman Kevin McCabe said: "I think most of the Premier League clubs and other football clubs support us over this injustice that has come about this season.
"Four years ago the Blades had just lost in the Championship play-off final and I felt gutted. This time I feel cheated. I think there is a consensus that most clubs support an injustice so I hope we will get the vast majority of clubs in the Premier League supporting our case."
Wigan chairman Dave Whelan, whose side survived at the Blades' expense, is backing their action.
He said: "Charlton, Sheff United, Wigan, Fulham and Middlesbrough are all determined that we should get justice and West Ham should have been deducted points.
"It has to be done quickly because the longer this goes on the less likelihood of the league reviewing it at all.
"We are going to fight and support them, we will fight with them to the end."