After their 6-1 defeat of Granada, Costa has admitted that he's placed his future in Atletico Madrid's hands this summer.
The forward has been linked with a move away from the club, who have brought in Luis Suarez in his position.
"I've let the club decide my future," Costa said after Sunday's win over Granada.
"At no point did I want to fight to be a burden here, on the contrary.
"I've made it very clear to the club.
"I was listening if they were going to sell me, if there was the chance to go out on loan, I'd leave.
"If they wanted to rescind my contract, I'd also have accepted that.
"I spoke to the club, the boss.
"I made it very clear what was happening, that I'm going to fight and keep fighting and that if injuries allow, I'm going to be here, but if there was a possibility I would leave, I'd leave.
"I'm at their disposal."
On the arrival of Suarez, Costa couldn't understand why Barcelona had left him leave.
"We have a player like Luis who, luckily [for us], left Barcelona," Costa added.
"I don't know how a team like that lets him leave.
"In the end, it's very good for us.
"He gives us a lot with his goals, his fighting spirit in the dressing room and his will to win and win trophies."
Many have speculated about whether Diego Simeone will play Suarez and Costa together up front.
"It's very good," Costa said on the prospect.
"One biting and one fighting."