The Spain international was heavily linked with a move to China's lucrative top flight in January but decided to stay at Stamford Bridge.
Costa has not scored in his last five Premier League outings and that poor run of form has led to increased speculation that he has become distracted by further doubts around his future.
There are some reports in England claiming that the 28-year-old has been offered a staggering $1,106,000-per-week contract to tempt him to move to the CSL at the end of the European season.
Shu Yuhui, the billionaire owner of Tianjin, has now claimed that a deal for Costa is in the pipeline and has vowed that the club will challenge the likes of Real Madrid and Bayern Munich for the world's best players in the transfer window.
"I can only say that we are still working on the deal [to sign Costa]. And we have already made contacts with several players," he told Sina Sports.
"We have high standards [in buying foreign players] and those players prefer top clubs such as Bayern Munich and Real Madrid. It's safe to say that we have the same transfer targets as those illustrious clubs.
"We may have to pay bigger price because our club are now competing with Real Madrid and Bayern Munich."
Chelsea sold Oscar to Shanghai SIPG for $102 million this season and Carlos Tevez reportedly earns the highest wage in world football – $1,046,000 per week – at Shanghai Shenhua.
Chinese sport's governing body stated in January that they would look to impose a salary cap to prevent clubs from spending unreasonable sums of money on foreign stars.
However, this has not stopped players from being linked with mega-money moves to the CSL, with Arsenal's Mesut Ozil and Bayern Munich's Douglas Costa among those rumoured to be attracting interest.
Tianjin, coached by Italy's World Cup-winning former captain Fabio Cannavaro, won promotion to China's top flight in October.