Roberto Mancini's side have experienced a revival in recent weeks and can record a third straight league win for the first time since November 2012 with victory at struggling Cagliari on Monday.
The former Manchester City manager returned to the club in November, following the departure of Walter Mazzarri, and has overseen a climb to 10th position.
Back-to-back wins against Palermo and Atalanta halted a run of three straight defeats, before Inter squandered a two-goal lead to draw 3-3 at Celtic in the UEFA Europa League on Thursday.
Despite sitting 10 points behind third-placed Napoli in Serie A, club legend and vice-president Zanetti has been encouraged by Mancini's impact, and feels the club should set their sights on the top three.
"Obviously, there are still areas where we can improve, but I think our two Serie A wins in a row and good result in Glasgow will give the team confidence," Zanetti told the Deejay Football Club radio show.
"It wasn't easy to strike the right balance, but Mancini is working hard to get us playing a certain way. He loves the club, and results are starting to come now."
He added: "It's going to be very tough to get third place because there are a lot of teams ahead of us. We have to give it a go though – we've got nothing to lose."
Cagliari, on the other hand, have developed a losing habit this season and are without a win in their last three, leaving them 18th in the table, three points from safety.
But Gianfranco Zola's side will take confidence from their previous meeting with Inter, in September last year, when Albin Ekdal's hat-trick fired them to a shock 4-1 success at San Siro.
Mancini's men are a different proposition now, however, having scored seven times in their past two league games with Fredy Guarin and Mauro Icardi in particular beginning to show what they are capable of.
Rodrigo Palacio has been in fine form, too, scoring twice against Celtic, but doubts remain over his ankle problem, while Jonathan and Yuto Nagatomo are still sidelined long-term.
Reports also suggest that Nemanja Vidic could be on his out of the club following disagreements with Mancini, and he could miss out along with Lukas Podolski.
Antonio Balzano is unavailable for the hosts due to injury as Cagliari bid for a first clean sheet under Zola.
