Real Zaragoza president Agapito Iglesias insists coach Jose Aurelio Gay's job is safe.
But Iglesias said: "There is no problem with Gay. We know he has done a good job and will continue for the remainder of the season, but we will have to see how things are going in January.
"We are second-bottom. I know the fans are concerned, as is everyone at the club, but the staff is committed and giving their all on the field.
"We ask that you let us do our work because we have players and a coach to move forward, and we have known from the beginning that the goal is to remain in the top flight."
Iglesias hit out at press reports claiming the club were intent on dismissing Iglesias and were lining up a replacement.
"The news that has come in terms of signing coaches is on unsubstantiated information," he said.
"It is completely untrue. Within this club we call for professionalism and journalists should show the same."