The Spain international is ready to return to Atletico, despite their summer market transfer ban meaning he won't be eligible to play until the New Year.
Costa is pushing for a deal from his end, while Atletico have now shown their hand.
The offer has left Chelsea disappointed, particularly after turning down over €85 million in January from China's Tianjian Quianjian.
Intensifying negotiations between the two clubs is Costa, who is reluctant to turn up for preseason at Cobham.
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