The Blues are one of a host of Premier League sides, including Manchester United, said to be tracking the Germany international, who’s £20m BVB release clause is due to kick in at the end of the season.
The likes of Real Madrid and Barcelona are said to be after Reus, with a move in the summer rumoured to be the most likely outcome.
But, Jose Mourinho has told Chelsea owner Roman Abramovich that the versatile forward is his top target, with a move this month a possibility as the Londoners look to win the race.
Schurrle, who operates in a similar role to his compatriot, is likely to make way.
Bundesliga side Wolfsburg are understood to be keen on the pacey 24-year-old, while there are claims that Dortmund themselves are interested.
Schurrle helped Germany to World Cup glory over the summer, yet he’s been an infrequent first-teamer for Chelsea this term, making just five Premier League starts.