Costa claimed last week that Chelsea boss Antonio Conte had informed him in a text message that he was not part of the Italian's plans going forward at Stamford Bridge.
That came at the end of a season when Costa scored 26 goals in 46 games for the Premier League champions, but which also saw persistent speculation about the Spain striker's future - with a possible switch to China being widely mooted.
The 28-year-old has now ruled out any chance of moving to the Far East as he does not want to jeopardise his World Cup hopes, but he also concedes that trying to stay and fight for a starting place at Chelsea - with whom he has a contract until 2019 - is a waste of time.
He told the Spanish media after scoring in Spain's 2-1 World Cup qualifying win over Macedonia: "Things don't work like that. The fight for a place has to be fair.
"When there is a fair fight you stay and fight but if there isn't then you have to go."
Chelsea have been linked with a move for former striker Romelu Lukaku from Everton and Costa accepts that Conte might want to move him on in order to bring in a new first-choice centre-forward.
However, he also suggested that things could have been handled differently.
Costa said: "You need to ask Conte what has happened, he's the coach and if he has the option of signing someone else and doesn't want to have problems with a senior player then that's normal.
"But there are ways of saying things, ways of doing things.
"Thanks to God I'm not lacking teams (to join). If Chelsea don't want me I will choose the best option for me."
One of those options appears to be a return to Atletico, who Costa played for before joining Chelsea in 2014 and a club which remains close to the Brazilian-born striker's heart.
Atletico recently lost an appeal against a FIFA-imposed sanction which means that, while they can still buy players this summer, the Spanish outfit will not be able to register or play them until January.
With next year's World Cup finals in mind, that may put players off joining the Rojiblancos ahead of the new season, but Costa does not see it as an insurmountable problem for him.
He added: "I have a contract with Chelsea for two years. If they decide to sell me I will search for the best choice of team for me.
"Atletico are among those teams. Signing for Atletico wouldn't mean not playing, I could go (on loan) to some team in Spain, in Italy, in Brazil...wherever I can continue playing.
"Everyone knows that Atletico is a club that I have a lot of love for. Regardless of if I return or not, I'm always going to continue loving them.
"Now we have to wait to see how things turn out."
A move to the Chinese Super League is not in Costa's plans, however, with the former Real Valladolid forward adding: "I rule out China, I have to think about my future. I have to think about the World Cup. If I fight and I do things well I'll have every chance of going to the World Cup. I cannot go to China."
