The Swiss squad is fighting with Force India to maintain sixth place in the standings, the Hinwil-based team 15 points ahead.
After finishing in 11th place in second practice, Kobayashi said it will not be easy to keep the Force Indias behind this weekend.
He said, however, that Sauber's form is better than in the last race.
"Although we look better than we did at the Nurburgring, I have the feeling it will be tough to catch the Force India cars, but we want to get in front of them in tomorrow's qualifying," said Kobayashi.
"The balance of my car is not really brilliant yet, but I think we can improve that. For me the soft tyre is the difficult one up to now, so I prefer the super-soft."
Team-mate Sergio Perez, 12th quickest, also believes Sauber is stronger than in Germany last weekend.
"I think we have a better pace here than we had recently at the Nurburgring, and I also believe the ambient temperatures, which are supposed to get higher, will help us to do a better qualifying as it is crucial to get the super-soft tyres to work then," Perez said.
"On the long runs I had degradation with both compounds, but with the soft the balance was better compared to the super-soft. For me the soft tyres were also more consistent than the super-soft. I believe it will become quite an interesting weekend for all of us in regard to the tyres."