The Germany international has long been linked with a summer move to Stamford Bridge and following the conclusion of the Bundesliga, admitted he expects to leave for west London
News emerged in April that the two clubs had been involved in discussions for the 22-year-old, who has scored 14 times for Leverkusen this season.
However, with rumours emerging that a potential makeweight in the deal for Schurrle, Kevin De Bruyne, has instead set his heart on a permanent move to Champions League finalists Borussia Dortmund, the deal for the Germany international appears to have been delayed.
"We'll see. Certain things were promised to me," the forward told reporters following his side's 1-0 win at Hamburg on the final day of the Bundesliga season.
"I hope they will keep these promises. It also depends on Leverkusen. I think, it was my last match."
However, perhaps hinting at the difficulties in securing the young Belgian De Bruyne, Leverkusen's sporting director Rudi Voller revealed no deal had been done yet with the Europa League winners for Schurrle.
"Let's all stay cool. We said it is only possible, if we find a proper alternative."
Schurrle has seven goals in 22 appearances for the German national team and was a member of Joachim Low's Euro 2012 squad last summer, when he started the quarter-final victory against Greece.