Croatia centre-back Benkovic has made two senior appearances for the Foxes since arriving from Dinamo Zagreb in August 2018.
The 23-year-old's latest loan move, which is subject to international clearance, follows spells with Celtic, Bristol City and Cardiff.
He spent the first half of this campaign with the Bluebirds but was restricted to just one Sky Bet Championship outing.
Benkovic, who has been capped once by his country, started Leicester's 2-0 FA Cup third-round win over Wigan last January, having made his debut as a substitute in a 4-0 Carabao Cup success over Fleetwood shortly after joining the club.
Leuven and Leicester are both owned by King Power International Group.
The Belgian club, who sit fourth in the Jupiler Pro League, last week signed former Foxes midfielder Andy King.