He would be the second signing of the London Club as they already agreed a deal to sign Ajax winger Hakim Ziyech.
The report added that Werner has a 55 million euro ($62.45 million) release clause which expires on June 15.
Chelsea reportedly had offered the 24-year-old a contract worth 200,000 pounds per week.
Werner is second-top scorer in the Bundesliga this season with 25 goals.
His goal record is four behind Bayern Munich’s Robert Lewandowski.
Werner has also made 29 appearances for Germany, scoring 11 times.
Liverpool are the first to be linked to the 24-year-old.
But time appears to be running out for the Reds.
The forward’s release clause expires on June 15 — two days before the Premier League is set to restart after a coronavirus-enforced break of several months.