The Leicester Mercury claim the 23-year-old, who is the brother of Manchester United forward Romelu Lukaku, will put pen to paper on a deal with the Foxes in the coming weeks, despite interest from a number of other clubs.
Rumours of the full back's potential departure began after he was absent from Lazio’s pre-season training squad earlier this month.
Claude Puel already has Ben Chilwell and Christian Fuchs as options at left-back, but the addition of Lukaku could be one for the future as the latter has confirmed his intention to leave the King Power Stadium upon the expiry of his contract, due at the end of next season.
The Foxes were linked with a move for German left back Marvin Plattenhardt earlier in the transfer window, but it seems Lukaku is now their number one target.
Lukaku only started ten Serie A games last season, but ended up making 44 appearances across all competitions, with the majority coming off the bench.
Should he join, Lukaku will link up with a host of new signings in the east Midlands. Jonny Evans has joined from West Brom, Ricardo Pereira has signed from Porto and Norwich starlet James Maddison has arrived at the Foxes in a mammoth deal worth up to £25m.