Toure looks likely to leave the Etihad stadium outfit 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 St 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.”
Motta, 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.
Meanwhile City’s stars are no longer the best paid in world sport, according to new figures released this week.
The Global Sports Salaries Survey for 2015, compiled by the sportingintelligence website in association with ESPN The Magazine, reveals Paris St Germain have taken over top spot with an average first team salary of £101,898 (€142,000) per week.
City topped the poll in 2014 but their weekly average of £96,445 has seen them fall to third place behind Real Madrid.
Five Premier League sides make the top 20 with Manchester United at number six, Chelsea eighth, Arsenal at 10 and Liverpool at 14.
The GSS Survey considers solely the earnings for playing sport, not for endorsements or other extra-curricular activities. The 2015 report surveyed 333 teams in 17 leagues across 13 countries in seven sports: football, baseball, basketball, American football, cricket, ice hockey and Australian Rules football.
1 Paris St Germain £5,298,693 (£101,898)
2 Real Madrid £5,040,520 (£96,933)
3 Manchester City £5,015,122 (£96,445)
4 Barcelona £4,715,116 (£90,675)
5 Los Angeles Dodgers £4,679,937 (£89,999)
6 Manchester United £4,679,377 (£89,988)
7 Bayern Munich £4,468,643 (£85,935)
8 Chelsea £4,353,056 (£83,713)
9 New York Yankees £4,263,577 (£81,992)
10 Arsenal £4,054,066 (£77,963)