The Austrian youngster has impressed for Red Bull Salzburg since making his first-team debut in 2010.
The Liverpool Echo reports that Brendan Rodgers is set to step up his efforts to land the Austrian under-21 international in January.
Liverpool signed defenders Kolo Toure, Aly Cissokho, Tiago Llori and Mamadou Sakho this summer, but are still keen to add to their defence in January.
Liverpool face competition from Arsenal and Juventus in the battle to sign Hinteregger. The Italian side have watched Hinteregger in action in recent weeks.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.