The Brazil-born star has been in sensational form this season, bagging 12 goals in his opening 10 games and it is thought that Mourinho’s admiration of the player could see him make a bid in the next transfer window.
Any compulsion to make a move will be added to by his current front-men’s dubious Premier League contributions, with Fernando Torres, Demba Ba and Samuel Eto’o notching just one league goal between them so far this term.
And Costa, who is set to represent Spain at next year’s World Cup, could prove the perfect remedy, as the North London outfit look to secure their first league title since 2010.
A prospective move is unlikely to be cheap, however, after the 25-year-old signed a new deal in the summer, an agreement that could see Atletico demand over £35m for the player.
As a result, Mourinho would need significant financial backing from Chelsea owner Roman Abramovich in order to land his man.