Jose Mourinho is understood to be a big admirer of the young Schalke midfielder, who featured against the Blues twice in this season’s Champions League.
Arsenal are among a host of top clubs linked with the young German, but Mourinho has been boosted by the news that Schalke are interested in Chelsea’s Belgian youngster Kevin De Bruyne.
De Bruyne is looking to leave Stamford Bridge in January, after failing to nail down a regular first team place under Mourinho.
He previously shone in the Bundesliga while on loan at Werder Bremen, where his performances caught the attention of Schalke manager Horst Heldt.
“Kevin De Bruyne is a class player who is interesting for many clubs,” Heldt said.
Chelsea may now look to offer the Belgian in part exchange as they look to lure Draxler to Stamford Bridge, an offer which may well prove the most attractive to Schalke.
“The fact that a number of clubs are in the hunt for Julian Draxler , is still the case,” Heldt added.