Tevez was in inspirational form for the Hammers in 2007 as they avoided relegation from the Premier League and Sheffield United went down after a dramatic last day.
The Blades were furious with the outcome, claiming the Argentine should have been ineligible to play because of a third-party ownership row.
The saga has been rumbling on for almost two years, with Sheffield United initially lodging a claim for as much as £45million - the figure they estimated as the true cost of relegation.
West Ham rated the loss at no more than £5million but an independent Football Association tribunal last year agreed with the South Yorkshire club's claims.
It appears a settlement of around £10million - spread over a period of five years - has now been struck and Hammers manager Zola is pleased that the end is in sight.
ConfidentThe Italian said: "I hope it will be resolved soon and I am confident it will be.
"It's looking good at the moment and it would be a good thing for the club - because then we can sit down and plan for the future, knowing exactly where we are and what we are dealing with.
"I believe they are trying to find an agreement, and I hope they do that as soon as possible. That would give us a clear picture for the future, and we can sit down and plan."
Zola insists that he has no problems getting on with his job despite constant speculation about the Tevez issue and the financial state of the club.
He explained: "I personally have to focus on the work on the pitch. That is why the club employed me.
"I'm 100 per cent focused on my job. It is my responsibility to make sure things on the pitch work well. If I can do that I can be helpful to the club.
"This is the world of football. I know it is not just about kicking the ball for us right now; it is dealing with other things. But whatever the worry, I know I can switch on to the football and not let other things get in the way."