Claudio Ranieri is hoping to strengthen the Foxes' options heading into the second half of the season.
Red Bull Salzburg want around £10m for the centre-back who has previously been scouted by Arsenal, Liverpool and Manchester United (via Mail).
The Foxes had previously been interested in a move for the 23-year-old's teammate for the Austrian national team, Aleksandar Dragovic, however the club appear to have now pulled out of a deal for Dragovic, and have decided to focus their attention on his countryman, the Mail claims.
While the other three sides that have previously watched Hinteregger may have larger reputations, the defender will most likely know that a switch to the King Power Stadium will probably offer the most first-team action. Joining Leicester would also see the defender link up with another international teammate Christian Fuchs.
The 29-year-old is Austria's current captain, so may well have something to do with the Foxes' recent interest in two of the country's best defenders. And he may well still have a part to play if Hinteregger needs any convincing that a switch to Leicester is the right move for him.