Serie A side intend to bid for Manchester United man
Antonio Conte, who was appointed as the Nerazzurri's manager earlier this month, is keen for Lukaku to spearhead his side next season.
However, Inter will first have to sell Mauro Icardi to raise the required funds to land the Belgium international.
Icardi would fetch around £60m in the market, with Juventus keeping close tabs on his sitaution.
And Conte, who wanted to sign Lukaku while he was Chelsea boss, wants to spend the proceeds on the former Everton attacker.
Lukaku only scored 15 goals for United last term, having struck 27 times in his debut campaign at Old Trafford.