The RB Leipzig forward - who reportedly has a £54 million release clause - had been linked with Liverpool and was "proud" of being associated with such a move, but it now appears he could be heading to the London club.
According to BBC Sport, league leaders Liverpool aren't interested in signing Werner, who has scored 11 times in 29 games for Germany.
If the Blues are able to get a deal over the line, it would make the striker their second signing for next season, having already completed a £37 million move for Ajax winger Hakim Ziyech back in February.
Meanwhile, Chelsea have also been boosted by French star Olivier Giroud signing an extension to remain at the club for another year.
During the January transfer window, manager Frank Lampard was linked with both Napoli's Dries Mertens and PSG superstar Edison Cavani, but neither move materialised in the end.