According to Italian publication Il Tempo (via Sport Witness), Lukaku is 'probably' going to sign for the Foxes this summer, with a deal between the two sides reported to be 'close'.
The news will come as a blow to West Ham, who had hoped to sign Lukaku in a double deal alongside his Lazio teammate Felipe Anderson but reportedly baulked at the Italian club's asking price, rumoured to be in the region of €70m for the pair.
However, a shock third party could be set to enter the race: Manchester United. Lukaku's older brother Romelu is of course one of the stars of Jose Mourinho's side and Rome newspaper Il Messaggero claim the striker has asked his manager to sign the younger Lukaku this summer.
Lukaku has been left out of Lazio's squad for their pre-season tour, perhaps the biggest sign yet that the 23-year-old will shortly be plying his trade at another club sooner rather than later.
West Ham should be able to cope despite their apparent failure to land Lukaku this summer, with the club already able to choose from Aaron Cresswell and Arther Masuaku in the left-back position.
The Hammers have also been linked with a move for Borussia Dortmund winger Andriy Yarmolenko as new manager Manuel Pellegrini attempts to shore up his squad ahead of his return to the Premier League.