According to Football London, Lukaku is ready to sign a five-year-contract as soon as negotiations between the two clubs are completed.
Chelsea are preparing a revised bid of at least £100million for the Belgian striker, which they expect Inter Milan to accept.
This would potentially break the British transfer record set yesterday by Jack Grealish’s move to Manchester City.
Once the price is finalised, Lukaku will return to Stamford Bridge on a deal rumoured to be worth £212,000-a-week.
Inter Milan are under pressure to sell players to help address their rising debt, but have only moved Achraf Hakimi on for a sizeable fee so far this summer.
The Moroccan wing-back, who arrived at the San Siro last July, joined Paris Saint-Germain for £51.3million at the end of a title-winning season in Italy.
Milan Skriniar, Stefan de Vrij, Nicolo Barella and Lautaro Martinez are other valuable assets being closely monitored by several clubs as the transfer window nears its conclusion.
But Lukaku emerged as their preferred target after an excellent two years in Serie A, during which he scored 64 goals in 95 appearances across all competitions.
He originally joined Chelsea as a teenager in 2011 but was given few opportunities, failing to score in 15 games.
Lukaku, who grew up supporting the club and idolising Didier Drogba, is keen to put things right in his second spell.
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