He added: "Our hope is that he will resolve his situation as soon as possible and that he can compete, train and play, which is what he likes doing the most and what interests the national team".
A pre-season move failed to materialise and Costa opted to remain in Brazil rather than return to training, but with a departure close, the 28-year-old insists he bears no ill will because "everything is cool".
The sale of Costa isn't unexpected after the striker's falling out with Chelsea manager Antonio Conte towards the latter half of the 2016/17 PL season.
Atletico, though, will only be able to register Costa when their transfer ban expires in January.
Atletico have announced that they have reached an agreement, believed to be worth around £50m, to sign Diego Costa from Chelsea. He scored 59 goals for the Blues, 52 of them in Premier League play.
The Spain international has been in fantastic form for Chelsea last season.
Conte was predictably asked about the forward on Friday, but stone-walled any questions. The pressure is now all on the shoulders of David Luiz to be the South American funnyman in the dressing room.
Despite all negativity and nasty rumors, Costa's stint at Chelsea was a success. The forward has got his dream move and the Blues have got a new number nine in Alvaro Morata.
"Now it is not important, I am not interest to continue talking about this issue".