The striker has been linked with a move away from Manchester United, where he has struggled for form since the appointment of Ole Gunnar Solskjaer, with San Siro having been touted as a possible destination.
The 26-year-old striker posted a photo of himself in California on Instagram, beneath which Nainggolan commented: “Tot snel” – ‘See you soon.’
It’s also possible that the remark could be a reference to a meeting between United and Inter in the International Champions Cup on 20 July.
The two sides are due to face each other in the annual pre-season tournament at the National Stadium in Kallang, Singapore.
Lukaku is reportedly preparing to turn his back on English football to try his hand in Italy, and talks are believed to already be underway between United and Inter.
The 26-year-old is currently away enjoying his summer break after finishing his spell on international duty earlier this month.
Nainggolan quit Roma to join rivals in Inter 12 months ago, but there has been speculation that the Serie A giants will look to offload the Belgian along with Mauro Icardi this summer as part of a major overhaul under new manager Antonio Conte.
The 31-year-old retired from international football last summer after being left out of Roberto Martinez’s squad for the World Cup in Russia.
Nainggolan’s Inter teammate Icardi has been told irrefutably that he is not in Conte’s plans, with the former skipper having been frozen out of the team completely over the last six months.