The Manchester United captain is understood to have multi-million pound offers from clubs in the Chinese Super League.
The 31-year-old has struggled to command a regular place in Jose Mourinho's United side.
Superstar strikers who could replace Wayne Rooney at Man United
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Who could replace Wayne Rooney if he left Manchester United
And with the transfer window in China open until next week, Mourinho refused to guarantee Rooney will still be at Old Trafford next month.
But Cannavaro, who won the World Cup with Italy in 2006, admits that although Tianjin made an approach for Rooney, a deal is unlikely.
He told Tianjin TV: “We did make an approach for Rooney, but it was just a chat because he simply doesn’t suit our style of play.
Manchester United's Wayne Rooney
“No further discussion was necessary."
Cannavaro also revealed Tianjin were snubbed by Borussia Dortmund's Pierre-Emerick Aubameyang but remain hopeful of signing Fiorentina’s Nikola Kalinic.
He said: "The truth is we had more frequent contact with Aubameyang.
Tianjin Quanjian boss Fabio Cannavaro
"Unfortunately, our bid was rejected by Borussia Dortmund who said he was needed in this season’s Champions League.
“Our prime target is still Kalinic but it’s quite difficult for his club to let him leave at the moment.
"Under such circumstances, we are caught in a dilemma. I need to communicate with our managing director.”