Upon his return to Italy from London, Ausilio said he negotiated with United officials over a possible deal to acquire the Belgian forward, who Inter reportedly want to sign on a two-year loan deal with an obligation to buy.
"We had a meeting with Man United for Lukaku," he said. "It has been an official approach between two important clubs. Let's see. (Manager Antonio) Conte wants every player we're trying to sign."
Previous reports indicated that Inter have offered an initial €10-million payment to begin the loan this summer, followed by €30-million installments in 2020 and 2021.
Inter apparently believe United could be averse to dealing with them after the Premier League side's failed €45-million bid for Ivan Perisic two years ago.
Lukaku was conspicuously absent from United's training session on Thursday during their preseason tour in Australia, according to Rob Dawson of ESPN FC.
Despite manager Ole Gunnar Solskjaer's preference for Lukaku to stay, the 26-year-old is said to be worried about his role in the team as Marcus Rashford could see an increase in starting opportunities at his expense.