Marca says Costa previously allowed his representative, Jorge Mendes, to sign a deal which would see him move to Stamford Bridge this summer.
But the deal also included a penalty clause for Costa, understood to be several million euros, if the move failed to be completed.
The report also claims Costa began to have doubts over a move to Chelsea and was hopeful of agreeing a new contract at the La Liga champions.
However the penalty clause in the deal meant Costa would face paying a substantial fee to scrap his proposed switch to the Premier League and has resigned himself to leaving Atletico for Chelsea.
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