The Belgian is closing in on a sensational return to Chelsea, seven years after leaving for Everton, in what would be a club-record £97.5million deal.
Lukaku completed a medical in Milan before flying to London on Monday evening.
Official confirmation of the move could come on Tuesday, with Chelsea in Belfast on Wednesday for their Uefa Super Cup showdown with Villarreal at Windsor Park.
Speaking at the airport, Lukaku told Sky Italia: “I’m gonna send a message [to Inter fans] soon.”
Lukaku, who scored 64 goals in 95 games for Inter, was happy at the Serie A champions and not anticipating a departure.
However, interest from Chelsea intensified over the past week and the striker made his intention known the the Inter hierarchy, leaving the club’s fans up in arms.