The 25-year-old Swedish forward has impressed in the Bundesliga this season, after moving from Malmo to RB Leipzig two years ago.
With Sadio Mané heading off to the African Cup of Nations this month, Jurgen Klopp is keen to bring in cover and, with Borussia Dortmund unwilling to discuss a move for Christian Pulisic, Forsberg seems to now be top of the New Year wish list.
Source: DSG