After a win and two draws, Deportivo stood sixth in La Liga heading into the weekend, with their opponents already struggling in the bottom three.
But Aranzubia said it was important to guard against complacency.
"Things have been going fairly well but things have to improve and if we lose in Granada everything is going to look different," he said.
"We are pleased with how we started, but we have not done anything extraordinary and we need to keep our feet on the ground.
"All teams in the league are strong and although Granada have not had a good start I do not think that will burden them."
After Sunday's game, Deportivo host Sevilla before making a trip to the Bernabeu to face Real Madrid. But Aranzubia stressed the focus was firmly on consolidating their good start this weekend.
"I do not look beyond the meeting with Granada," he added.
"This is the most important because it is the most immediate."
Granada earned a point against Sevilla but have lost their two matches either side of that result - the last being a 3-0 defeat by Real Madrid.
However, Gabriel Torje is confident with the right approach they can register their first win on Sunday.
"We will beat Deportivo if we do things right," said the Romanian winger, looking for his first start after three substitute appearances.
"If I start against Deportivo I'll be happy but if not I'll wait for my chance.
"I've done well with my national team [scoring twice goals and providing two assists in the recent World Cup qualifiers] and now I want to do well with Granada.
"I have time to prove that I'm a player."