Jose Mourinho is actively seeking an alternative to Fiorentina's Juan Cuadrado, a deal very much on the verge of collapse, and has identified Costa as his replacement.
But according to Tuttomercato, the West London club aren't willing to meet Shaktar's inflated valuation - and instead will lodge a £20m offer.
Costa fuelled speculation over his impending departure from the perennial Ukrainian champions when revealing it would be a 'dream' to play for Chelsea.
Newspaper Review - Friday 23 January
It would be a dream to play for Chelsea
He said: "I joined five years ago and I think it's time [to go].
"It would be a dream to play for Chelsea.
"It's a unique chance. I will try to negotiate."
Though far from prolific, Costa created a glut of assists to help Shakhtar to land five successive Ukraine Premier League titles.
He was signed at the tender age of 20 for a modest £4.7m fee and has three-years remaining on his contract.
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