The Daily Star says the Stamford Bridge side are keen to snap up the 21-year-old centre-back ahead of rivals Manchester City.
City are thought to be close to meeting the £17m release clause in the Greek international's contract, following talks with Schalke last month.
But the German side will welcome Chelsea's late interest, as it could allow them to demand even more cash for their coveted defender.
Liverpool are also keeping a close eye on developments, says BILD.
Is Papadopoulos capable of making it at Chelsea? Give us your shout below...