The 28-year-old Belgium striker is reported to have completed part of the medical in Milan on Monday, and be close to re-joining the Blues for a club-record fee of €115million euros (£97.5m).
The PA news agency has contacted Chelsea for comment.
Lukaku was with Chelsea for three years from 2011, the last two of which featured season-long loan stints with West Brom and then Everton.
He subsequently joined the Toffees in a permanent deal in the summer of 2014 and then moved on to Manchester United in 2017.
Lukaku scored 42 goals in 96 appearances for United across two seasons before then signing for Inter, for whom he has netted 47 times in 72 Serie A games, helping them win the title last term.
Lukaku is Belgium’s record scorer with 64 goals in 98 appearances.
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