The 20-year-old forward, who can play as a direct striker or out wide, has impressed this season for Bundesliga side Hamburg, and has caught the gaze of the Merseyside club.
The Asian starlet signed for Hamburg back in 2010, and has since grown in stature in Germany; he has started this season with four goals in seven appearances.
The Reds are short up front, with Luis Suarez and Fabio Borini the only recognised forwards in Brendan Rodgers’ squad after Andy Carroll’s loan move to fellow Premier League side West Ham.
The Italy international is yet to hit the back of the net in the Premier League this season, leaving added pressure on Suarez to get the goals.
Heung-Min would provide competition for places in the Anfield club’s attack, and allow Rodgers to rotate his forwards.