The Spain international spent two years with the La Liga side from 2012 to 2014 and scored 64 goals in the process.
However the 27-year-old was then sold to Chelsea for £32.5m and he has since gone on to find the net 35 times.
But, Costa is reportedly keen on a return to Spain and he has been linked with a move to Atletico.
However the club’s president, Cerezo, says that it would be near enough impossible to complete a deal.
“[Costa] has a contract with Chelsea,” Cerezo told Al Primer Toque radio show.
“Often, no matter how much you want a player, there is a contract. To negotiate with Chelsea can be really difficult, almost impossible.”