Sheffield United agreed an undisclosed out-of-court settlement with West Ham after an arbitration panel had ruled Tevez should not have been permitted to play in the final matches of the 2006/7 season, when the Argentina striker helped the Hammers avoid relegation at Sheffield United's expense.
The Blades' relegation in 2007 meant that Leeds missed out on additional payments in relation to Premier League survival for the transfers of striker Rob Hulse, defender Matthew Kilgallon and goalkeeper Ian Bennett.
Bates said: "We sold a number of players to Sheffield United with contingencies. When they got relegated on the last day of the season we missed out on a substantial sum.
"That's what we lost and if they are being compensated for their loss we believe we should be compensated for our loss.
"There are other clubs in the same boat who have similar claims. Our's is the biggest claim and it would be nice to collect that and strengthen our squad. We are currently taking advice on it and won't be commenting further at this time."