On Sunday, Costa will be presented to Atletico fans, along with fellow new signing Vitolo, with the Copa del Rey tie against Llieda slated for his debut.
However, everything will hinge on Chelsea and the Premier League completing the transfer paperwork in time.
AS says nothing can be rubberstamped until the selling club and their federation gives the all-clear - which could mean Blues officials tying up loose ends over the weekend.
Costa, who was 'sold' by Chelsea to Atletico in September, hasn't been able to register due to their transfer ban, which ends on January 1. The striker is now training with the first team squad and now only lacks match fitness.