The Reds have already had an enquiry rejected for the Swedish winger.
The Reds made an enquiry about the Swedish international last month, but were swiftly turned away by his current club, who are not keen on a sale.
Jurgen Klopp is reportedly keen to add wingers to his squad, with them seriously lacking in that department, and Forsberg’s performances in the German league in recent seasons have caught his attention.
Indeed, he was named Swedish midfielder of the year in 2014, another indication of how well he has performed for his side.
A move in January looks unlikely though, with his current clubs not willing to sell having only secured him from Malmo last January.
Instead, the Reds will continue to track the player and may their move in the summer transfer window, according to the Daily Mail reports.
Liverpool’s scouts are likely to be impressed by what they have seen so far this season though, with Forsberg having managed five goals in 11 league appearances so far this season.
That far surpasses Klopp’s current option, Jordon Ibe, who is yet to get himself on the score sheet in the Premier League this season.