They wanted to take the player on loan in the summer, but the move was blocked by Brendan Rodgers.
However, Benkovic has not gotten a look in at Leicester all season.
It means that he could be available for the right move, according to his club boss.
Rodgers told reporters: "It depends [Benkovic leaving in January].
"If there's the right team for him and there's the right possibility then of course we will look at that.
"He stayed behind, he's offered us really good cover, he's been involved in some of the Under-23s games, so he's been playing football.
"We'll see how that develops over the course of January."