According to the Liverpool Echo, the Reds are now contemplating a bid for the German striker.
Werner is regarded as one of Europe's top young strikers and several clubs are keeping tabs on him, including German giants Bayern Munich.
But Liverpool are reportedly expecting to lose Daniel Sturridge and possibly Davick Origi too, and the Reds will need to bolster their attack.
RB Leipzig are all but resigned to losing their star striker who has 14 goals so far this season.
"It’s well known that we want to extend with him, but he’s signalled to us that he does not want to sign a new contract," Leipzig chief executive Oliver Mintzlaff said.
"We need to see what’s right for us and for Timo."
Werner's contract runs out in a year and the battle between Liverpool and Bayern may well be more about wages and oppurtunitues, rather than transfer fees.
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