While Tianjin owner Shu Yuhui admits his side are still interested in signing the Spain worldwide, but have their sights set on other high-profile targets.
The 28-year-old has scored just three times in 12 appearances for Chelsea, who have also seen their lead at the top of the Premier League table cut to just four points.
The Chinese Super League outfit are believed to have been the club to offer the Brazilian a deal worth £600,000-a-week back in January.
Costa is again being linked with a move to Tianjin Quanjian this week.
The departure of Costa would fuel rumours of a return to Chelsea for Everton striker Romelu Lukaku, who has made it clear that he will not sign a new contract with the Goodison Park club.
He told Sina Sports: "I can only say that we are still working on the deal [to sign Costa]".
And Yuhui suggested that his club will continue to try and tempt top players to join his club, saying: "We have high standards [in buying foreign players] and those players prefer top clubs such as Bayern Munich and Real Madrid".
'We may have to pay bigger price because our club are now competing with Real Madrid and Bayern Munich'.
He's gone five games without a goal since netting against West Ham in March, his longest Premier League goal drought all season.
Tianjin already has a number of well-known footballing names on their books with Fabio Cannavaro holding down the position of manager, while Alexander Pato and Axel Witsel arrived at the club following their promotion from the second division.