The Blues striker, who was forced to train alone amid reports of a bid for his services, may well have to readdress his plans, having seemingly been keen for a move to the Far East.
The ambitious side already have Axel Witsel, Jadson and Geuvanio in their ranks, meaning they are reportedly unable to sign another overseas player.
Tianjin were also chasing Edinson Cavani, Karim Benzema, Radamel Falcao and Raul Jimenez, but the new restriction that kicks off when the new Chinese Super League season starts in March, means that they will have to scrap any future signings unless they release one of their foreign imports.
Yuhui told Tianjin TV: "If [the rule] had been '4:1' as in the past, then we would have made a big investment this year, but now it seems to be changed to three.
"This situation has brought a change to our signing plans. The online reports about Costa, it's true we'd like him, and we made an offer for Cavani and were deep in negotiations."
He added that they wanted to sign Costa in January rather than wait until the end of the season.
"We couldn't afford to wait half a season," he explained.
"We continue to wait and suffer, but at the end of the day, we'll get someone.
"We have targeted a lot of strikers, and made an offer for Benzema, but with this policy change, we are very helpless."