According to a report in Saturday's edition of Il Tempo (via Sport Witness), the Foxes are in pole position to capture the signature of the 23-year-old Lazio defender.
Manuel Pellegrini's West Ham were heavily linked with a move for Lukaku, but were priced out as Lazio demanded a €70m fee for a douple swoop involving Lukaku and Felipe Anderson.
West Ham have received heavy criticism for their transfers in recent seasons, most notably after former Sporting Lisbon president Bruno de Carvalho famously labelled David Sullivan and David Gold as the 'dildo brothers'.
Having reportedly been priced out of several targets over recent years, history looks to be repeating itself as Leicester close in on their man.
Italian newspaper Il Tempo now report that Lukaku, younger brother of Manchester United striker Romelu, is 'probably' going to sign for the East Midlands side.
They say a move is so close that the defender will not join up with Lazio for their upcoming pre-season tour.
The 23-year-old played 44 times across all competitions for Lazio last season, scoring just once as his side finished fifth in Serie A and qualified for the Europa League group stages.
Despite Leicester not being able to offer European football, it could be the best destination for Lukaku in the long-term - as the left back position looks to open up in the not too distant future.
Christian Fuchs has previously announced that he will leave the King Power Stadium once his contract expires next summer, while England Under-21 international Ben Chilwell did not have the most impressive of seasons last term.