The France international was famously left hanging in Paris as the summer transfer deadline fell as he waited for Chelsea and Sevilla to reach terms over a fee for his signing.
TMW says Chelsea managing director Marina Granovskaia has revived contact with Sevilla in recent days.
And a new €55m cash offer has now been tabled for Kounde.
For his part, the Frenchman has always left the door open to moving to London, despite August's frustration.
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