Despite already receiving proposals from Manchester United and Barcelona, Werner, the Germany forward, would prefer to move to Anfield where he can link up with compatriot Jurgen Klopp.
And RB Leipzig are not against cashing in on their star striker given he has a clause in his contract which means he can leave for £51million this summer.
However, there is a condition to this clause, The Athletic claim.
The £51m deal must be agreed by a deadline in April for the transfer to go through at the end of the season, as this gives Leipzig time enough to sign a replacement for Werner ahead of the start of the 2020/21 campaign.
They would have around four months to bring in a new forward rather than the month-and-a-half were Werner to not secure his exit until the transfer window opens in July.
Liverpool are no strangers to opening negotiations for summer signings early, the report continues.
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They began talks to sign Fabinho, the midfielder, and goalkeeper Alisson in March, and if Klopp signs off on a swoop for Werner discussions will begin in the same month this year.
The Reds are not alone in chasing Werner, who has 27 goals this season, however.
As well as the aforementioned interest from Man United and Barcelona, Chelsea are also known to be long-term admirers of the 23-year-old.
Timo Werner wants to join Liverpool and is holding out for the Reds to make a formal approach for him, reports claim.