Inter are in talks to sign the Belgian striker, who was in and out of Ole Gunnar Solskjaer’s first team last season.
Lukaku’s agent, Federico Pastorello, met Nerazzurri white-collars earlier this week but his client has urged him to accelerate negotiations.
The 26-year-old is currently holidaying in Los Angeles but will report back to Carrington training ground on Monday for the start of pre-season.
He does not want to be lingering around the Manchester area too long, though, and hopes a deal is done before United fly to Australia.
Their first match Down Under is against Perth Glory on July 13, meaning Lukaku hopes to be donning blue and black in two weeks’ time.
On the matter, Pastorello said: “Lukaku is a dream (for Inter) and it is not an easy deal to realise.
“For me, nothing is impossible. Romelu has expressed his plans and wishes. Let’s see.”
United bought Lukaku from Everton for £75million in July 2017 and want to recoup as much of that fee as possible.
The chunky frontman has scored 42 goals in 96 appearances for United, failing to convince United fans and management.
Old Trafford chiefs are holding out for £75m and want as much of the money up front, presumably to fund their summer exploits.
Inter seldom splash that kind of money and may have to sell Mauro Icardi, who was stripped of the captaincy last season, in order to raise the funds.
Antonio Conte, who was appointed head coach of the Serie A club in May, tried to sign Lukaku for Chelsea in 2017.
The Italian tactician’s admiration is reciprocated, with Lukaku recently branding Conte “best manager in the world”.
Lukaku said last season it would be a dream to play in Italy, having grown up watching the world’s hottest stars grace the country’s top flight.
“Playing in Serie A is a dream, it would be really a dream,” he said on Sky Italia’s Lords of Football in April.
“I hope to be able to play sooner or later, even if at the moment I am focused on the United.”
