The 26-year-old is said to be new Nerazzurri boss Antonio Conte's preferred choice for his main striker, and Inter sporting director Piero Ausilio has confirmed that the clubs are in talks over the Belgium worldwide.
The Frenchman was also pictured when Manchester United unveiled their home strip for the upcoming season, which was inspired by the club's 1999 Treble-winning heroics.
"We'll see what happens".
Inter wanted to sign Lukaku on loan with an obligation to buy, perhaps splitting payment across several years.
Inter's push could become more hard as United are not in any rush to sell the Belgian forward.
To make matters worse, Lukaku was caught by Sky Sport's cameras yawning while on an exercise bike next to Anthony Martial at the WACA Ground.
Antonio Conte, the Inter coach, believes his club's chances of signing Lukaku are likely to hinge on being able to offload Mauro Icardi to free up cash but there have yet to be any takers for the Argentina striker, despite some interest from Juventus.
Last season ended with just two wins from the final 12 games and Solskjaer is keen to get off to a flying start when the new campaign kicks off against Chelsea on August 11.
The 26-year-old - in Australia for the club's pre-season tour - scored 15 goals across all competitions as United finished sixth in the Premier League and lost to Barcelona in the Champions League quarter-finals.