The 28-year-old was the subject of interest from Asia during the January transfer window, with Tianjin Quanjian claiming they launched a bid for the forward.
Costa was subsequently left out of Chelsea's 3-0 victory over Leicester City but has since returned to the first-team squad, featuring in his side's last two Premier League games against Hull City and Liverpool.
However, Spanish source Cadena SER reported on Friday that Costa has reached an agreement to head to the Chinese Super League at the end of the season.
But Costa has reacted angrily to the claims in an Instagram post, writing: “They talk too much shit!!! Come on Chelsea.”
Chelsea boss Antonio Conte also played down the reports in his press conference ahead of his side's Premier League clash against Arsenal on Saturday.
The Italian said: "I don't know, but every week I hear a lot of news and a lot of speculation about Diego.
"I think now the most important thing is to be focused on this championship and we are in a good position.
"Diego is an important player for us and he is happy. This is the most important thing. The summer is a long way away."
Costa is the current joint-top goalscorer in the Premier League alongside Arsenal star Alexis Sanchez, having netted 15 times for Chelsea so far this term.