The Chinese Super League club tried to sign Costa during the January window, but their owner Shu Yuhui has confirmed that talks to take Costa to China are still continuing.
Tianjin are believed to be ready to make Costa the best-paid player in the world, by offering him a contract worth £650,000 a week after tax.
Costa’s £150,000-a-week Chelsea contract runs out in the summer of 2019.
He has scored 17 Premier League goals this season, but only three this year.
Tianjin are seventh in the Chinese Super League table after five games. They are managed by Italian World Cup winner Fabio Cannavaro and signed Alexandre Pato for £15 million from Villarreal in January.
The Chinese Super League season starts in March and ends in November. The mid-season transfer window is open from June 19 to July 14.
