Jovetic's first season in English football was blighted by injuries and a loss of form as the 24-year-old made just six starts in all competitions following a £22m move from Fiorentina.
Consequently, Inter were strongly linked with luring the Montenegro international back to Italy, but Ausilio claims that City were unwilling to part company with their player.
"Some weeks ago there was contact with Manchester City and they told us that the player is not on the market," he told Sky Sport Italia.
"So we thought that this is no longer an opportunity, even if the market closes on September 2."
Jovetic scored seven times for the Citizens in 20 first-team appearances last season.