The Spain international could be on course to return to the Vicente Calderon when the transfer window reopens, according to Mundo Deportivo.
Costa has struggled to replicate the goalscoring form of his debut season at Chelsea this term, netting just four times so far. The 27-year-old's relationship with Chelsea boss Jose Mourinho is also rumoured to be strained after the forward reacted angrily to being substituted during the 0-0 draw at Tottenham Hostspur last weekend.
This is not the first time that Costa has been linked with a return to Atletico, the club he spent four years at before signing for the Blues in 2014.
