The 23-year-old has been in excellent form for his German club during the 2019-20 campaign, scoring 25 times and contributing 10 assists in 30 appearances in all competitions.
Liverpool have been strongly linked with the Germany international in recent months, and according to Italian journalist Nicolo Schira, the Reds are now closing in on a deal for the forward.
Schira claims that Jurgen Klopp's side are ready to pay the €58m (£48m) buy-out in Werner's Leipzig contract before the clause expires in April.
Chelsea, Manchester United and Bayern Munich have also previously been linked with the former Stuttgart youngster, but Liverpool are now seemingly nearing an agreement ahead of a summer move.
Werner has scored 86 goals in 145 appearances for Leipzig in all competitions, in addition to netting 11 times in 29 appearances for the German national team.