The Atletico striker missed his side's 1-1 draw at home to Malaga on Sunday, but now looks set to return in time for the Rojiblancos' Liga decider at Camp Nou on Saturday
The Brazil-born Spain international missed Sunday's 1-1 draw at home to Malaga as he continues to recover from a thigh problem, but trained in the gym on Monday and is expected to step up his routine later in the week.
Costa worked alongside goalkeeper Thibaut Courtois, while midfielder Cristian Rodriguez was put through his paces outside as he returns from a hamstring injury.
Coutois took a knock in Sunday's game at the Vicente Calderon but will definitely start at Camp Nou on Saturday, while coach Diego Simeone is also confident Costa will play a part.
"He is progressing well," the Argentine coach said of his side's top scorer on Sunday. "We'll have to see how he is ahead of the match."
If fit, the 25-year-old striker, who has 36 goals in 50 appearances for Atleti this season, will likely appear for the last time in La Liga ahead of a proposed summer move to Chelsea.
The former Valladolid and Celta Vigo forward will also be named in Spain's provisional World Cup squad on Tuesday.