The Ivory Coast international is likely to leave the Etihad Stadium this summer after five years with the club.
Inter, managed by former City boss Roberto Mancini, are reportedly leading the race to acquire the 32-year-old.
When asked about the ongoing negotiations, Zanetti said to Gazzetta dello Sport: “We are at the stage where we hope we can complete it.
“Yaya would give us that leap in quality.”
Zanetti also revealed Inter are keen to bring Paris Saint-Germain midfielder Thiago Motta back to the San Siro this summer.
The Italy international played three seasons for Inter before joining PSG in 2012.
“If Motta were to arrive, he could give so much,” Zanetti said.
“He knows the club, he has experience, quality and is one of the strongest midfielders that I have ever played with. He is very intelligent.
“To bring players like them would give us that leap in quality.”
Toure, who is reportedly City’s highest earner on around ??220,000 per week, has scored 10 goals in 28 Premier League appearances for City this season.
The former Barcelona midfielder signed a four-year contract with City in April 2013.
Motta, meanwhile, is out of contract at PSG next season and has made 24 league appearances for the Ligue 1 champions.
Inter have endured a disappointing campaign but are hoping to qualify for next season’s Europa League.
The Nerazzurri are eighth in the standings, four points adrift of Genoa, who hold the last European qualifying spot with two games remaining.