However, Tianjin have not lost their interest, and billionaire owner Shu Yuhui insists a deal is still in the pipeline to bring the Spanish global to the club.
Monaco teenager Kylian Mbappe could be on his way to Real Madrid this summer, which would pave the way for Chelsea to sign Alvaro Morata.
It may well be more than just a coincidence that Costa's drop off came after speculation of a move to China in January, as the goals started to dry up after Antonio Conte dropped him for the trip to Leicester City.
The Spain global was the subject of interest from the Chinese Super League in January, though the Blues turned down an £80million offer for his services at the time.
Tianjin are reportedly ready to make Costa the best-paid player in the world, with a contract worth £650,000 a week after tax.
'We have high standards [in buying foreign players] and those players prefer top clubs such as Bayern Munich and Real Madrid.
He's gone five games without a goal since netting against West Ham in March, his longest Premier League goal drought all season.
"I can tell you the players we want are also the targets of these clubs, so we have to pay bigger price to beat them".
Chelsea are now four points clear at the top of the Premier League and face Tottenham, who are second in the table, this Saturday in the semi-final of the FA Cup.
Tianjin splashed £15 million on Alexandre Pato - formerly of Chelsea - from Villarreal in January and are keen to make more strides in their next transfer window.