Recent speculation has linked him with Chinese Super League club Tianjin Quanjian.
After losing the FA Cup final to Arsenal despite scoring his team's goal, however, he told Spanish media that former club Atletico Madrid were the only team he would leave for.
"If the club want to sell me, there's one club I'd move to," he was quoted as saying, agreeing that it was Atletico, who he left three years ago to join Chelsea.
"I will remain (at Chelsea) if there is intention from the club and the coach for me to stay, but if they want to sell me to bring in another striker, I will go."
It will not be to China, he insisted.
"People talk too much, people talk about China but there's a World Cup coming up and if I go to China I won't have the chance of going to it."
Costa, Chelsea's top scorer as they won the Premier League this season, played two games for Brazil in 2013 but switched to Spain a year later after being granted Spanish citizenship and represented them at the 2014 World Cup.
(Reporting by Steve Tongue in London and Richard Martin in Spain; editing by Clare Lovell)
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