Inter last won the title in 2010 and have not played Champions League football since 2011-12, and Zanetti credits the team's impressive showing to the work of head coach Luciano Spalletti, who made the switch to San Siro from Roma in the close season.
But Inter great Zanetti, who is now the club's vice president, believes it is still a tall order to win the league this term.
"We are demonstrating great consistency," he told Corriere dello Sport.
"With the Scudetto, there are sides that are better equipped, but thanks to Spalletti and the other guys there is great enthusiasm around the team now.
"Winning is always very difficult, but I think the most important thing for us is that we are proving to be protagonists.
"The objective is to qualify for the Champions League, because the Champions League is an important showcase and makes you grow as a club.
"This year we have started to lay the foundations for the future, which will allow us to be competitive again. That is the role this Inter should always have.
"It takes a team, but equally important for those who work outside the camp. Along with the fans, we must always be on the same wavelength to take Inter back where it belongs."
Zanetti is rightly considered as one of the greatest full-backs to have graced Serie A and the former Argentina international highlighted the man he sees as one of the best in the position playing today.
"Everyone has their own characteristics," he added. "But I would say Alessandro Florenzi at Roma.
"I like his professionalism, the way he reads the game and the passion he puts into everything he does."