Costa, who helped Atletico win their last La Liga title in 2014, has struggled to make an impact since returning to the club from Chelsea in 2018. The 32-year-old has six months left on his contract.
The Spain international’s second spell with Atletico has been repeatedly disrupted by injuries and he has recently returned from a spell out due to deep-vein thrombosis.
Costa converted a penalty in a 3-1 win over Elche on Dec. 19 and he came off the bench late in the 2-0 victory over Real Sociedad three days later.
But he was absent on Monday from Atletico’s first training session after the Christmas break, ahead of Wednesday’s game at home to Getafe. Spanish newspaper AS reported that Costa had asked to rescind his contract immediately for family reasons.