Schalke had originally denied receiving a bid from the Serie A champions for Draxler.
But according to Sky Sport Italia, a bid of £16.8m has come in for the 21-year-old.
It is thought negotiations will take place.
However, the report suggests long-standing Chelsea target Axel Witsel is also an option.
The Blues are keen on the Zenit St Petersburg midfielder as they seek to strengthen their squad after an unconvincing start to their Premier League title defence.
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Julian Draxler could leave Schalke before the window closes
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