The Brazilian-born Spain international starred for the Rojiblancos before signing for the Londoners in 2014, firing them to an unexpected La Liga title and the Champions League Final in a stellar campaign.
Costa then made a bright start to life at Chelsea as he played a big role in their Premier League success, but the combative forward has endured a turbulent 2015/16.
Rumours of his discontent at Stamford Bridge have been widespread of late, and there have even been suggestions that the player himself is eager to move back to Atletico.
And now reports claim that Simeone has made signing the 27-year-old a priority for the coming transfer window as he looks to add a source of goals to his ranks in a bid to challenge for the Spanish title next term.
Costa is Atleti’s main target, but Alexandre Lacazette, Edinson Cavani and Gonazlo Higuain are also being looked at.