Fernando Vazquez's men have found form at the right time to pull clear of danger, last week securing an impressive 4-0 victory at Levante.
However, with still just two points separating them from Real Zaragoza in 17th place, the goalkeeper insists there is still some work to do.
"We will not be saved even if we win over Bilbao," he told a press conference.
"There is much work ahead, as the situation is still difficult."
Bilbao are currently six points ahead of Deportivo in 14th place, but could yet be dragged back into the relegation dogfight.
Aranzubia added: "The Lions have a tough schedule. Next week they face Barcelona and if they have lost against Deportivo, then they would just be three points away, so you can understand their concerns."
Midfielder Bruno Gama also maintained no-one should get carried away despite Deportivo's recent run of good form.
The Portuguese said: "We know it is difficult to maintain this level, but we will work every day to keep winning.
"We are always looking to do more, and we want to continue like this."
Depor could have veteran forward Riki available again, but will still be without Colombia midfielder Abel Aguilar and Spain defender Carlos Marchena.
Athletic were beaten 3-0 at home by Real Madrid last time out, which was a second straight defeat leaving some work still to do for Marcelo Bielsa's men if they are to steer clear of the relegation dogfight.
Defender Mikel San Jose is an injury doubt for the trip to the Estadio Riazor, as is forward Ibai Gomez.