Talks have been ongoing between the Premier League club and the German side over a potential 22 million euro player-swap deal, which would see Kevin De Bruyne move in the other direction.
With a disappointing domestic campaign, by the club's lofty standards, coming to a close, Chelsea is already looking ahead to next season, and Ingo Haspel, Schurrle's agent, has claimed the 22-year-old Schurrle could be a Blues player very soon.
"I am waiting for information from either Leverkusen or Chelsea, but there could be some positive news by the end of this weekend," Haspel told reporters. "It is an indication of how much Chelsea want the player that they are continuing to negotiate."
Schurrle has 11 goals in 30 Bundesliga appearances for the Werkself and has attracted the attention of a number of European clubs this season, with Chelsea looking to bolster its attacking options next season.
A potential spanner in the works for the Blues, however, is that they appear reluctant to part with De Bruyne just a year after signing him, while the likes of Borussia Dortmund and Schalke are also keen on the Belgium international.