Chelsea have already opened negotiations for the German international, who has struck 18 goals in 17 Bundesliga appearances so far this season.
Liverpool boss Jurgen Klopp is a long-time admirer of the 23-year-old goal-machine and was keeping his powder dry for the summer before making any bids for the player.
But Chelsea’s move in the January window, following the lifting of their FIFA transfer ban, has triggered immediate interest at Anfield.
Werner has already expressed a desire to play in the Premier League, although it is still likely that RB Leipzig, who have a great chance of ending the season as Bundesliga champions, will attempt to keep Werner until the summer.