Yet after another double on Saturday stretched his tally for the season to 17 and helped Chelsea demolish Swansea 5-0 to move five points clear at the top, the odds are swiftly shortening on the Spaniard achieving both ambitions.
"More important than my goals is the team winning," Costa told Chelsea's official website.
"Of course, it is nice to be the top scorer but when I came here my aim was to win the league."
This would have been music to the sensitive ears of his manager Jose Mourinho. He wants great players but to him, great players have to be team players.
So rather than hail the brilliant individual contributions of Oscar and Costa, who scored two apiece within 36 minutes at Swansea's Liberty Stadium, Mourinho reckoned he only wanted to talk of one-for-all excellence.
"I prefer to say the team played very well," he said. "It was the perfect game." So perfect after Oscar had put them ahead in just 49 seconds that, astonishingly, even Mourinho could find nothing to complain about.
Fitting then that the victory should again be delivered by a man you would imagine fits Mourinho's idea of the perfect identikit player.
For as well as being skilfully hawk-eyed, Costa was once again selfless, industrious, feisty and up for a scrap. So good, indeed, that he could even be forgiven trying to look fearsome while wearing those twee blue gloves bearing the Chelsea crest.
Even with Chelsea four up and yawning at the start of the second half, he was still snarling in defenders' faces as irritably as Mourinho himself can get up referees' noses.
His double put him three goals clear of Sergio Aguero in the race to finish as the league's top scorer.
As for the title, though, Mourinho is taking nothing for granted.
"There is no history without titles. If we play fantastically well but don't win cups I think in 20 years nobody will remember this team," he warned.
For him, it is all about the collective. Yet some individuals make all the difference. Inspired by a man built in his own combative image, Chelsea look unstoppable.
(Writing by Ian Chadband, diting by Pritha Sarkar)
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