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.
However, their owner, Shu Yuhui has confirmed that talks to take Costa to China are still continuing.
The Spain worldwide was heavily linked with a move to China's lucrative top flight in January but chose to stay at Stamford Bridge.
NAIJ.com understands that Tianjin Quanjia have come back with an offer to make Costa the highest paid player in the world on £34 million a year after tax.
Former teammates Oscar and Ramires have already made the move and are enjoying the fruits - and by fruits we mean money - of China.
"However, the best players want to go to clubs such as Bayern Munich or Real Madrid".
'We may have to pay bigger price because our club are now competing with Real Madrid and Bayern Munich'.
Reports in the United Kingdom have indicated that Tianjin - who signed Costa's ex-Chelsea team-mate Alexandre Pato for £15million from Villarreal in January - want to make Costa the highest-paid player in the world with a contract worth £650,000 a week. It's safe to say we have the same transfer targets as those illustrious clubs.
Tianjin, under coach Italian Fabio Cannavaro and with the likes of Brazilian Alexandre Pato and Belgian Axel Witsel in their ranks, have made modest start to the new season with two wins and two draws from their first five games leaving them seventh ahead of Friday's meeting with Beijing Guoan.