Lukaku helped fire Inter to the Serie A title last season, their first since 2010, with 24 goals in 36 league games.
But mounting financial problems at the San Siro have already seen Antonio Conte step down as manager and several players leave the club.
Chelsea believe that Lukaku could be persuaded to come back to the Premier League and rejoin the club he first signed for 10 years ago.
Despite impressing at both clubs, Jose Mourinho was happy to sell Lukaku to the Toffees for £28million as he chose to rely on more experienced players.
It proved a costly mistake, as Lukaku’s value soared during a prolific spell at Goodison Park, culminating in a £75million move to Manchester United.
He fell out of favour after the appointment of Ole Gunnar Solskjaer and subsequently moved to Inter Milan, where he has scored 64 goals in 95 games.
With Timo Werner struggling last season and Tuchel seemingly unconvinced by Tammy Abraham, Chelsea are searching for striker who will give them that clinical edge to kill off opponents.
Lukaku, who is one of the most consistent goalscorers in world football for club and country, certainly fits the bill but would come at a huge cost.
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