Tianjin had Chelsea striker Costa, Paris Saint-Germain's Edinson Cavani, Radamel Falcao at Monaco and Raul Jimenez at Benfica in their sights until the authorities imposed limits on foreign players and wages, Shu Yuhui told Tianjin Sports TV.
Shu was quoted as saying by Sina Sports that Tianjin may now have to get rid of its current foreign star Luis Fabiano.
"There were talks about Costa. It is true we looked at him, Cavani as well," Shu was quoted as saying by Sina Sports.
He added that there had been "intense" talks, including with super agent Jorge Mendes, who went to Tianjin.
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"A few days ago, Mendes came to my hometown to meet me," Shu said.
"Just yesterday, (the club) was prepared to sign two players, the contracts were ready, the price and wages had been discussed, it was Falcao and Raul-Jimenez.
"The two players were ready to sign, and then we received the signal, the restrictions on the salary and the number of (foreign) players. We had no choice, we had to change our plans."
"Because of the special situation of his club, Diego Costa is in a similar situation, he can't leave before June. We can't wait so long, until mid-season.
Shu said a bid had also been made for France striker Karim Benzema at Read Madrid.
"With the change of policy (on foreign players), we are left helpless.
"We are now discussing whether or not to keep Fabiano."
China's growing financial football muscle has caused some alarm, with Tottenham coach Mauricio Pochettino saying at the weekend Chinese clubs had "broken" the market with astronomical transfers.
Chinese Super League teams will be able to field no more than three foreigners in a match when the new 2017 season begins in March, according to new Chinese Football Association rules.
Previously four non-Chinese players were allowed, provided one was from an Asian Football Confederation country.
The CFA said such a move would aid development of the game in a country whose leader, Xi Jinping, is determined to see China reach soccer superpower status.
The organisation has vowed to rein in the "recent appearance of irrational investments and the payment of high transfer fees and salaries for domestic and foreign footballers".
China are currently ranked 82nd in the world, but have only qualified for one World Cup, in 2002, where they failed to win a match or score a goal.