The 21-year-old was strongly linked with a move to Liverpool during the summer transfer window.
Reports even suggested that the young defender already had agreed a deal subject to a medical, but a move failed to materialise.
Schalke are reportedly prepared to sell Papadopoulos for around £11million in the January transfer window.
Manchester City, Chelsea, Inter Milan, AC Milan and Zenit St Petersburg are all reportedly keeping tabs on Papadopoulos ahead of January.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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