Gazzetta dello Sport claim Inter are prepared to submit an offer of €60m for Toure, who is under contract with City until June 2017.
"Who doesn't dream of having a player like him?" Fassone told Tuttosport. "Toure would give our midfield line something that we are lacking. But his wages and City's asking price might be a big obstacle."
Inter keen to keep trio
Inter are also working on new deals for their Argentina forward Mauro Icardi and Croatia midfielder Mateo Kovacic. Icardi is Inter's top scorer this season with 15 goals and is tied to the club for a further three seasons, while Kovacic, who is a reported target of Liverpool, is under contract with inter until June 2019.
"We are almost there with respect to Icardi's contract extension," Fassone said. "We want to keep him just as we want to keep Kovacic. We will evaluate with great care their eventual offers. It's clear that if we want to sign three players [this summer] we will need to evaluate those that will depart."
Inter's priority right now is to tie Inter goalkeeper Samir Handanovic to a long-term contract. The Slovenia international has been linked with Roma as well as Manchester United and becomes a free agent next season.
"Handanovic's renewal is an issue that we must resolve at once," Fassone said. "We need to understand what he wants. We cannot go into next season knowing that our goalkeeper's contract expires."
Inter are currently tenth in Serie A with ten rounds remaining.