And it has since emerged that Costa's agent, Jorge Mendes, travelled to China to hold talks over a move to big-spending Tianjin Quanjian.
Shu Yuhui, the club's owner, has revealed Mendes made a special visit to China to discuss a move for the 28-year-old, whose current contract expires in 2019.
'I made an appointment with (Jorge) Mendes and he came to my hometown to visit me,' he told Tianjin Sports Channel.
Tianjin were in the market for a top European striker until new rules implemented by the Chinese FA reduced the number of foreign players allowed to play at any given time from four to three.
'At that time, we were interested in signing Costa,' Yuhui added.
'PSG told us (Edinson) Cavani would only be allowed to leave in June, even though the player himself was willing to join us. The same can be said for Costa because Chelsea would only let him leave in June.
'However, the new season of CSL will almost reach the halfway stage in June, we can't wait so long.'