Tianjin Quanjian made a swoop for the Spain international forward last week, unsettling the 28-year-old to such an extent that he did not feature in the Blues' meeting with Leicester and trained alone until Tuesday after falling out with a fitness coach. The CSL side had offered Costa £30 million per year - a sum four times his current salary.
Atleti, who tried to re-sign the striker in the summer, have taken note, and will move if manager Antonio Conte is unable to resolve the situation. Costa had pushed for the move but the Stamford Bridge side held their ground and threatened to report the Spaniards to FIFA if they continued their pursuit.
However, Chelsea could use Costa against Hull City on Sunday and want him to continue to help them fight for the Premier League title until the summer - when they will reassess the situation.
Chelsea bought Costa from Los Rojiblancos in 2014 for £32 million and, although Atleti have the financial clout to re-sign their former player, they would struggle to compete economically with a Chinese Super League club or some of Europe's very elite teams.
Perhaps a greater impediment to any deal is a transfer ban hanging over the Spanish side that they are currently appealing against.
Barcelona have also been linked with a move for the forward, but they are not looking for a striker immediately as they focus their financial might on renewing Lionel Messi's contract after already securing deals to keep Neymar and Luiz Suarez at the club.
Paco Alcacer has struggled to breakthrough at Camp Nou, but both the club and the player are willing to be patient over his future after a €30m move from Valencia in the summer.
Meanwhile, the prospects of the Brazil-born attacker going to China are dwindling. Tianjin Quanjian's president, Shu Yuhui, has admitted that they are unlikely to return to sign Costa in the summer because his side will be halfway through their season, plus a rule change has made it more complicated to sign big-money players.
Chelsea, though, are willing to see how the situation develops before the end of the season.