That is according to the club's CEO Beppe Marotta, who has conceded that the Blues have the final say over the 30-year-old's future.
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The Belgium international returned to the Italian giants last summer on a season-long loan deal.
But he has struggled to recapture his form from his first spell at Inter between 2019-2021 where he scored 64 goals in 95 games to earn him a £97.5million transfer to Stamford Bridge.
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He has found the back of the net just 13 times from 33 matches in all competitions - with nine of his strikes coming in Serie A.
His inconsistent form has played a huge role in Inter fighting for a top four spot, leading to speculation that Inter will snub a permanent move for the ex-Everton star.
But club chief Marotta has hinted Inter would like to keep him, with the player also keen, though he stressed that the ball is in Chelsea's court.
It remains to be seen whether Lukaku is in incoming Chelsea boss Mauricio Pochettino's plans, with it known the Argentine is eyeing up a new centre-forward.
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Commenting on Lukaku's future, Marotta told Radio Rai: "Romelu loves the shirt he wears, he is very comfortable at Inter.
"These are fundamental aspects, this desire of his to be with us. But he is on loan until June 30.
"He will return to Chelsea, and we don't know what will happen on a technical level at that club.
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"At the moment we are at the window."
Despite Inter struggling in the league this season, they could still end up with two major trophies.
They face Fiorentina - West Ham's opponents in the Europa Conference League final - in the Coppa Italia final on Wednesday.
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And they will then pit their wits against Pep Guardiola's rampant Manchester City side in the Champions League final on June 10.
Though Lukaku will likely be left out of the line-up with all seven of his appearances in the European Cup this term coming from the bench.