
Conte saw his Premier League leaders triumph 3-0 at Leicester City without Costa, who was omitted amid reports of an argument with fitness coach Julio Tous and interest from clubs in China.
But the Italian insisted an injury was behind Costa's absence at the King Power Stadium and claimed any problems with his players will be dealt with within the dressing room.
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"I have read a lot of speculation about this topic. I can tell you if there are problems — and I repeat 'if' — with players, I am used to solving them in the changing rooms, not outside, not in press conferences," said Conte, who said he will assess Costa's fitness next week.
"Trust me, what I told you is the truth. If we start to think 'if an offer arrives, if, if, if ... I don't like to answer these types of questions. If, if. We must enjoy this victory. It wasn't easy to win against Leicester. It's important to respect our victory and our players after a good performance.
When pressed for more details, the Italian added, "If you want to know the truth, I'm ready to tell the truth. On Tuesday, during the training session, Diego stopped because he felt a pain in his back. From that moment he didn't train during the week. For this season today he wasn't available for the starting 11 or the bench."
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The former Juve boss also dismissed speculation of any offers from China for Costa, saying, "I don't know anything about this (offer from China). The club did not inform me about this. That can be only speculation."
And Conte claimed he will not concern himself with questions about Costa's future at Stamford Bridge after seeing his side open up a seven-point advantage over second-placed Tottenham Hotspur.
"I can't be concerned about this because today my players showed me a great performance and great spirit. That's very important. When you are able to win this type of tough game — Leicester were champions last season and this season I think their team has improved — it means that I can't be concerned about anything.
Conte coped with the loss of Costa by deploying attacking midfielders Willian, Eden Hazard and Pedro as a front three without a recognised striker.
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He said: "I think it's important to have another way of playing, playing without a No 9 is another solution. That's important. Sometimes changing your playing style is important during a championship."
Defending champions Leicester suffered a 10th defeat of their title defence but manager Claudio Ranieri praised his players' effort despite his side flirting with relegation danger.
He said: "I said from the beginning we have to look over our shoulder. We are in the battle for relegation. I said that two or three months ago. But we are in good condition and I'm sure now we can get some good points. I'm very happy with the performance. We tried to do our best."
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