The Blues have held a long-term interest in Schurrle and they were linked with a move for his services during last summer's transfer window.
Chelsea scouts are thought to have watched the Germany international in action against Schalke last Saturday and the 22-year-old impressed, scoring in the 2-0 win for Leverkusen.
Chelsea are thought to be keen on bolstering their attacking options in January as doubts continue to surround the long-term futures of Fernando Torres and Daniel Sturridge
Schurrle, who can play as a striker or winger, would fit the profile of the players Chelsea are trying to recruit and he could slot in with the style of the likes of Eden Hazard, Juan Mata and Oscar.
Bayer are keen to keep hold of Schurrle, but Chelsea could test their resolve with a big-money offer in January.