The Chinese Super League club have been linked with a mega-money move for the 28-year-old striker, who has two more years remaining on his Chelsea contract.
Costa scored 20 goals on his way to winning a second Premier League title with Chelsea since joining from Atletico Madrid for £32million in July 2014.
He has also been linked with a return to Atletico
He admitted previously to agitating for a return to Madrid before saying he was happy at Chelsea.
A statement on Tianjin's official website said: "During the past six months the club has not communicated with Diego Costa or his agent regarding his transfer to Tianjin Quanjian."
Costa has been linked with a £76m move but Tianjin insisted such a deal would be contrary to their strategy.
"We have no intention of becoming involved in any unhealthy competition and, consequently, paying a premium price," they said.
Costa earlier this month addressed the topic of his future, telling South American broadcasters DirecTV Sports: "I am the owner of my future and it does not mean that I am going to China."
Chelsea head coach Antonio Conte has insisted the "will of the player" is important in the future of any of his players.
Speculation over a move was at its height in January when Costa missed the trip to Leicester after apparently having his head turned by a mega money offer from Tianjin.
Conte publicly stated his absence on that occasion was due to a back injury and the rumours subsided but resurfaced earlier this month.
Chelsea can win a Premier League and FA Cup double with victory over Arsenal in Saturday's FA Cup final at Wembley.
Source : PA
Source: PA