The United striker Lukaku has emerged as a transfer target for Inter, who sent officials to England to try and reach a deal for the Belgian international.
Lukaku – contracted with the Red Devils until 2022 with the option of another year – joined United of Everton for £ 75 million in 2017 and the Premier League giants want to recoup that compensation as Inter-push for a first loan.
Ausilio returned to Milan on Thursday and told reporters: "We had a meeting with Manchester United for Lukaku.
"It was an official approach between two major clubs, we will see what happens.
"All the players we follow are goals we agreed with Antonio Conte, we want to meet his request within certain financial parameters."
Lukaku, who recognized the desire to play in Italy and hinted at his future, could have loved Old Trafford with United manager Ole Gunnar Solskjaer, who preferred Marcus Rashford, scoring 12 league goals last season.
The 26-year-old – in Australia for the club's pre-season tour – scored 15 goals in all competitions, as United finished sixth in the Premier League and lost to Barcelona in the quarterfinals of the Champions League.