Both boss Zola and assistant manager Steve Clarke refuse to take any notice of speculation concerning their futures.
Zola, 43, said: "I am the manager of West Ham and my focus is to get them safe — then we will see what happens. We are confident of staying up. We are improving and we are determined to keep fighting until the end.
"We know it's not going to be easy, but the determination and fight is there."
The Hammers are currently four points clear of the Premier League drop zone.
And like Zola, Clarke believes David Sullivan and David Gold will still own a top-flight club next season.
He said: "The best thing to do now is to get the points we require. We have to go to Liverpool on Monday and give a good account of ourselves.
"We focus on the next game, that is as far as we look at this moment in time.
"It would be silly for us to look any further ahead. We look for the next game and we get the points we require to keep West Ham in the Premier League."