Chelsea and owner Roman Abramovich are determined to keep the Spain striker, who has scored 14 Premier League goals in 19 games this season, despite reports of a falling out with head coach Antonio Conte.
Costa had been linked with a mega money move to Tianjin Quanjian, but the CSL club's owner on Tuesday said the new limit on foreign imports, with three permitted in matchday squads, could scupper a deal.
Tianjin's billionaire owner Shu Yuhui told Tianjin TV, according to Sina Sports: "This situation has brought a change to our signing plans.
"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.
"The online reports about Costa, it's true we'd like him, and we made an offer for (Edinson) Cavani and were deep in negotiations."
Shu, who recently met with Costa's agent Jorge Mendes, claimed he was interested in signing Karim Benzema of Real Madrid and Paris St Germain's Cavani.
Chelsea and PSG were reluctant to sanction a mid-season transfer, so Tianjin were looking elsewhere
China's transfer window is open until February 28 ahead of the season starting in March.
"We couldn't afford to wait half a season," Shu added.
Radamel Falcao of Monaco and Benfica's Raul Jimenez - two Mendes clients - had been set to move to Tianjin before the rule was introduced, Shu says.
"Mendes came to my home a few days ago and we also had ideas about Costa, but in the process were ready to sign two players, the contracts were done, the price was good - Falcao and Raul Jimenez," Shu added.
"The contracts were ready, the two players ready to sign, and then we get the news about the salary limits and restrictions on foreign players, so that made us change."
The news may be a boost to Chelsea's Premier League title hopes, but the subject of Costa's future will not go away.
The Independent on Tuesday reported that Atletico Madrid, Costa's former club, and Barcelona could try to sign the 28-year-old this summer.
The Brazil-born Spain striker signed a five-year deal on his arrival from Atletico in July 2014 for Â£32m.
Costa was repeatedly linked with a return to Atletico after being troubled by hamstring problems and disciplinary issues in his first two seasons at Stamford Bridge.
He has this season admitted he had wanted to leave, before stating he was happy, but it was widely reported on Monday that he recently rejected a contract extension on improved terms.
Costa's team-mates returned to training on Tuesday following two days off, when he trained alone.
Chelsea said the solitary sessions were part of his recuperation from a back injury and not related to speculation over his future.
Conte has refused to comment publicly on a rumoured disagreement and insisted Costa's absence from last Saturday's win over Leicester was due to the back injury which prevented him from training for three days.
The Chelsea head coach also said if there were any issues with players, he would resolve them behind closed doors.
Costa will be assessed to determine whether he can rejoin training with the first team.
Chelsea, who have a seven-point lead at the top of the Premier League, next play at home to Hull on Sunday.
Source : PA