The striker was pictured on Chelsea TV making his way out to training as Guus Hiddink prepared his squad for Sunday's FA Cup fourth-round tie at MK Dons.
Costa scored the decisive goal before withdrawing from last Sunday's Premier League win at Arsenal with a knee problem.
The club television channel also reported that Ramires bade his farewells to his team-mates at Chelsea's Surrey training base on Thursday after his move to Chinese Super League side Jiangsu Suning for a fee reported to be in excess of Â£20million.
Meanwhile, New York Red Bulls defender Matt Miazga was undergoing a medical with the Premier League champions, according to Sky Sports News.
Source : PA