The Brazil-born forward, who turned his back on the country of his birth to play for La Roja, netted 36 goals for Atletico in 2013-14 and has nine in nine appearances this term for the London club.
The 25-year-old has another chance to break his international duck when Spain play away to Slovakia and Luxembourg in Euro 2016 qualification this week and there is one very good reason why he should be optimistic he will end his goal drought: Chelsea and Spain team mate Cesc Fabregas.
Of Costa's nine Chelsea goals this season, four have been assisted by Fabregas, who is likely to be handed the playmaker's role by Spain coach Vicente del Bosque for the two qualifiers.
The former Arsenal and Barcelona man has seven assists overall, while the fact that of Costa's 19 shots this season 16 of them have been on target underlines the striker's excellent form.
Slovakia and Luxembourg, neither of whom are expected to qualify for Euro 2016, may be the perfect opponents for Costa to get his Spain career up and running.
There are still some doubts over his fitness but he said on Monday he was feeling fine after scoring a superb goal in Chelsea's 2-0 Premier League win against Arsenal on Sunday -- assisted by Fabregas of course.
"I always want to play when I am fine," Costa told reporters as he arrived at Spain's training base outside Madrid.
"When I am not feeling fine I can't play of course and there have been times recently (with Spain) when it would have been too much of a risk,” he added.
"I am desperate to score here and I have said to Cesc that we have a good connection at Chelsea, that we understand each other very well, but now we have to have it here too,” he said.
Costa will likely lead the line against Slovakia and Luxembourg, with Fabregas and the likes of Andres Iniesta and David Silva looking to provide him with the service on which he has thrived at club level.
Spain, the 2010 world champions, will be chasing a third consecutive continental title in France in two years' time if they qualify as expected from a pool that also includes Ukraine and Belarus.
They play Slovakia in Zilina on Thursday and take on Luxembourg in Luxembourg City on Sunday.

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