The 22-year-old Germany international is expected to leave the Bundesliga club this summer, with Chelsea strongly linked.
The Blues were thought to be interested in the forward last summer, but failed to complete a deal in time.
Chelsea winger Kevin De Bruyne could hold the key to an agreement this season. The Belgian international is wanted by Leverkusen as a makeweight in the Schurrle deal, but De Bruyne could scupper matters as he's thought to favour a move to Borussia Dortmund.
Still, Schurrle remains keen to seal a transfer away from Leverkusen.
Speaking to reporters following the 1-0 victory over Hamburg, Schurrle said: "We'll see. Certain things were promised to me.
"I hope they will keep these promises. It also depends on Leverkusen. I think it was my last match."
Leverkusen sporting director Rudi Voller issued a word of caution after the game though, warning Schurrle that no deal had been agreed with Chelsea yet.
"Let's all stay cool," said Voller. "We said it is only possible, if we find a proper alternative."
Unfortunately, Borussia Dortmund also see De Bruyne as a potential replacement for one of their top stars.
Jurgen Klopp's side will lose Mario Gotze to Bayern Munich at the end of the season, and are believed to have identified the former-Genk star as a like-for-like alternative.