Tuttosport says a bid topping the £100m mark would make them consider selling Lukaku, 28.
Inter paid a club-record £68m to sign the Belgian in 2019 and he has rewarded them with at least 30 goals in both his seasons in Milan.
And the Nerazzurri have reportedly repaid him with a salary boost from £125,000 to £140,000-a-week for the new campaign.
Borussia Dortmund star Erling Haaland is thought to top the Blues' transfer wishlist.
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