Barca's marquee signing from Liverpool has had to watch from the stands as his team mates have started the season after being suspended for biting an opponent biting during a World Cup match.
"I hope that Luis Enrique will be able to have all the players available. Up until now without him we have started the season well. Knowing the player I think that he will be ready for the Bernabeu," Zubizarreta told Spanish television.
"Suarez knows what stage he is at and the situation ahead of him. He will be an important player for us. The fans should be calm, the player realises what he did wrong and internally we have worked together,” he added.
Luis Enrique's side are still some way off the recent stellar years under Pep Guardiola but they have only dropped two points from seven games and lead the La Liga table.
Real are four points adrift and the pair meet at the Bernabeu on October 25 after Suarez's ban ends the day before.
Barca are looking to bounce back after a disappointing campaign in which all the major trophies eluded them, new Brazilian forward Neymar failed to shine and talisman Lionel Messi was far from his best.

Now the two are working well in tandem and proving to be a dangerous partnership with 13 goals between them in the league.
"It is an honour to play alongside Messi, he is the best in the world," Neymar said.
"It is amazing everything that he can do on the pitch: his passes, his runs and his goals. We are understanding each other better all the time and I am confident that we can develop it further to help Barcelona,” he added.
The main debate is how Suarez will fit into the attack and whether another highly talented player will improve the side or possibly lead to a battle of egos similar to Real Madrid's 'galacticos' a decade ago when the team lost their way.
The signs have been positive for Suarez, although he has plenty of pressure on his shoulders following his third biting bin.
He has arrived from a similarly competitive league in England and knows Barcelona because the parents of his wife Sofia living on the outskirts of the city.
Suarez has become friends with Argentines Javier Mascherano and Messi, the trio meeting up to sample the South American drink Mate together.
Suarez has received help from team psychologist Joaquin Valdes, who was brought in by Luis Enrique, over the anxiety that has played a part in him biting opponents.
Since mid-August Suarez has been able to train with his Barca team mates after the terms of his ban were eased but still he is unable to play competitive games and a highly-charged debut against Real will be a major test.
The only matches Suarez has played have been friendly games arranged by Barca and two for Uruguay.
He played against Saudi Arabia on Friday and scored twice in a 3-0 victory over Oman on Monday.

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