Spanish newspaper El Mundo Deportivo reports that Chelsea officials plan to watch Costa next week, with a bid potentially on the cards during the January window.
Atletico Madrid return from their winter break to face Malaga on Saturday 4th January - that will be Chelsea's first opportunity to watch the La Liga top scorer.
But the Stamford Bridge club can expect competition from a number of top European clubs, including several in the Premier League.
Arsenal, Liverpool and Borussia Dortmund are also likely to be watching the Brazilian-born forward, with each keen to upgrade their attacking options before the January deadline.
Chelsea boss Jose Mourinho is well aware of his talents from his time as manager of Real Madrid - Costa found the net in the Copa Del Rey final earlier this year against Mourinho.
Liverpool have also been heavily linked with the 25-year-old forward, who has scored 19 goals in the league already this season - one more than Cristiano Ronaldo.
The Chelsea and Liverpool target reportedly has a €36m release clause in his Atletico Madrid contract.