The Brazilian club made a bid for Tevez this summer after he expressed his desire to leave Manchester City, but ran out of time to complete a deal.
Since then, the 27-year-old Argentina international has made only two starts for City and was last week suspended by them following his alleged refusal to come on as a substitute in their Champions League defeat at Bayern Munich.
It has left his future at the Premier League club uncertain, but Edu - the former Arsenal and Brazil midfielder - says that as things stand, Corinthians are not thinking about renewing their interest in the forward, who left them to join West Ham in 2006.
"At the moment there are no plans to try and sign him again," Edu told the BBC.
"I'm starting to think about our new squad for 2012 and I've talked to our coach (Tite) about what we need - but Tevez was not mentioned.
"We are always interested in world class players like Carlos but you need to analyse if it's right for you at that time to try to sign him or not. We have not spoken to him or his agent."
Edu has been at the Leaders in Football conference in London this week, where Tevez's advisor Kia Joorabchian on Wednesday insisted the striker did not refuse to play for City in Munich, claiming that post-match comments by the player suggesting he had done so were mistranslated by a club interpreter.
Referring to the events in the Bayern match, Edu said: "It is very strange for me to hear that he refused to come on.
"Every player knows that sometimes you have to be on bench, you work for the team whether you're playing or not.
"They pay him to work for the team whether he plays or not. I was a player and I can understand that sometimes it doesn't feel good to be on the bench, but if he decided not to play that was a very bad decision."
He added: "As things stand, we have not considered going for Tevez.
"On Wednesday I spoke to our club president (Andres Sanchez) to see if he wanted me to make contact and start negotiations while I'm over in Europe but he said no, it's up to you to decide.
"Of course, that could change. It's nice to be over here to see the real situation of Tevez and speak to people about him.
"Then we can start to decide if it's right for us to try again.
"I was talking to Manchester City in July and we tried to buy him for 40million euros but the negotiations were not easy.
"We needed to arrange bank guarantees and other things. To organise all of that in two or three days (before the Brazilian transfer window closed) was very difficult. That's why we lost him."