The new contract keeps Werner at the club until 2023 but includes a release clause of €60m, which is expected to decrease over time.
According to Bild in Germany, Liverpool are Werner's preference should he leave Leipzig.
Having scored 20 goals in 18 appearances in the Bundesliga this season, Werner is catching the eye.
Chelsea have been reported to be interested in signing the 23-year-old as they hunt for a star centre-forward.
However, the Blues are keen to land Werner this month, which has all but been ruled out by the player himself.
The report claims that Werner's playing style would suit that of Jurgen Klopp's Liverpool.
Julian Nagelsmann's Leipzig side play with a similar fast-paced press and counter game to Liverpool's.
Werner's pace and intelligence are cited as counting in his favour when fitting into a Klopp side.
Liverpool are also reported to have a very healthy relationship with Leipzig following the transfer of Naby Keita in 2018.
The Reds are reported to have paid over the odds for Keita as well as allowing him to stay at Leipzig till his contract ran out.
However, Werner feels the Premier League is special.
"The Premier League is simply the most interesting league, you have to honestly say that," he said.
"It has got a certain flair to watch the English league and play there."
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