The 22-year-old has been the subject of intense transfer speculation in recent months, with suggestions that the Germany international will play in the Premier League next season.
Chelsea owner Roman Abramovich has been credited with an interest in bringing Schurrle to Stamford Bridge, with a fee of £20million mooted as the amount needed to tempt the Bundesliga club into selling.
Bayer Leverkusen are also keen to take Chelsea loanee Kevin de Bruyne - who is currently enjoying a season-long spell in Germany with Werder Bremen - as part of the deal, and it's understood that negotiations between the two clubs are almost finalised.
"I am waiting for information from either Leverkusen or Chelsea, but there could be some positive news by the end of this weekend," confirmed Schurrle's representative, Ingo Haspel.
"It is an indication of how much Chelsea want the player that they are continuing to negotiate."
Schurrle's transfer to west London cannot be formally completed until the transfer window reopens on July 1, but it seems that Chelsea are looking to get their summer business done early, even before announcing a permanent replacement for interim boss Rafa Benitez in 2013/14.