Costa has been training alone in his hometown of Lagarto, Brazil and insists he has no intention of returning to London unless he gets his wish to join Atletico.
Chelsea have fined Costa more than £300,000 in wages and will continue to do so until he ends his exile.
They have considered taking legal action against the player should he stay away.
But his lawyers have countered by claiming Chelsea have ruined his career prospects and will consider their own action.
Atletico are understood to be willing to offer £41million with a further £9m in add-ons which would represent a profit on the £32m Chelsea paid for Costa but is still short of their initial £60m valuation.
Costa received a text from Chelsea manager Antonio Conte saying he was no longer in his plans and has set his mind on a return to former club Atletico who are under a transfer embargo.
Real Betis and Deportivo La Coruna have offered to take him on an initial loan but he has so far refused those proposals.
Atletico’s embargo runs until January although the Spanish club can sign Costa after the window has closed on the agreement he cannot be registered to play until the New Year.