The Serie A side finished in a disappointing ninth place last season, but the 39-year-old believes that they will be closer to the summit this time around.
"I expect to see a competitive Inter," Zanetti told Inter Channel. "We have an obligation to return to the top.
"Inter are a team battling for important objectives. The pre-season is going well and we have a good reason to believe we'll do well once the season starts.
"President [Massimo] Moratti will do what's good for the club, as he always does."