Ausilio met with United officials in the UK on Thursday to discuss a potential deal for the Belgium international, who favours an exit from Old Trafford.
He told reporters: "We had a meeting with Manchester United for Lukaku.
"It was an official approach between two important clubs. We'll see what happens.
"All the players we're following are targets we've agreed with Antonio Conte. We want to satisfy his request within certain financial parameters."
Inter are hoping avoid breaking Financial Fair Play rules by signing Lukaku on loan with an obligation to buy or through player exchange.
However, United are not budging on their demand of a £75m fee.