The Italian was confirmed as the Blues' new manager on Monday and will take over when he steps down from the Italy national team following this summer's European Championships.
And it seems he wants Lukaku to spearhead a squad overhaul this summer, the forward likely to cost in excess of £50 million after leaving Stamford Bridge for Goodison Park in 2014 for £28 million.
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The Belgium international has thoroughly impressed this campaign with 18 goals and six assists yet the Toffees languish 12th in the Premier League and with only a glimmer of hope of securing a place in Europe.
Lukaku's desire to play in the Champions League is well documented, which he once again reiterated in a recent interview.
"Yeah of course, that’s the next step for me," he said. "I’m 23 next summer and I think it would be nice to play in the Champions League next season."
The striker's agent, Mino Raiola, and his father, Roger Lukaku, have both voiced their support for a move too, the latter publicly stating he wants his son to join Manchester United or Bayern Munich.
Assuming Everton will indeed miss out on the Champions League, then, it appears Lukaku's departure is a question of when and not if. Where he will find himself plying his trade next season is an entirely different story, though.
A return to Chelsea would not only infuriate the Goodison Park faithful but arguably benefit him little, given the Blues are also due to miss out on Europe's elite competition next campaign.
Lukaku received much praise for choosing to leave Chelsea in search of first-team football, so to complete a dramatic U-turn would likely see him vilified.
For Chelsea, however, signing a player of Lukaku's quality would be an excellent acquisition amidst a season where goals have proved hard to come by for the club's strikers.
The Belgian would provide competition for - if not replace - Diego Costa and certainly supersede the likes of Loic Remy and Radamel Falcao, who seem destined for moves away this summer.