While Liverpool have long been linked with an approach for the Germany international, recent reports have suggested that the Premier League leaders have opted against making a bid during the next transfer window.
That has seemingly reopened the door for Chelsea, who are known to be interested in players who can play in more than one position in the final third.
According to Bild, Rudiger has made contact with his compatriot to speak about signing for the Blues ahead of next season.
Although Werner has a release clause in the region of £50m, Chelsea can afford to pay big money for the 24-year-old after the sale of Eden Hazard last summer.
As well as featuring alongside each other for Germany, Rudiger and Werner were teammates at Stuttgart in 2015. body check tags ::