Costa, who was reportedly involved in a training-ground bust-up last week and the subject of a mega-money offer from China, put in a man-of-the-match show in Sunday's 2-0 win over Hull in the Premier League.
And Conte, who praised the 28-year-old for his performance, said Costa is happy at Chelsea, and wanted to put an end to any exit talk.
Conte said in his post-match press conference: "Diego has two years left on his contract at Chelsea. I think his contract puts an end to speculation.
"I repeat that he is very happy to stay at Chelsea. For us, it's very important to be concentrated in the present.
"I don't know [if he will be offered a new contract] - this is a decision that will have to be taken with the club."
Conte had earlier told Sky Sports after the game: "His performance was good, and I am pleased... for this reason, he started the game.
"During the press conference before the game against Hull, a lot of people asked me about his form, about his attitude, and I told them that I will take the best decision for the team. And I think after his performance that I made the best decision.
"It is normal to receive a lot of questions about it, but the most important thing for us is the answer that we give on the pitch. For the player, for me, the club, our fans, for the league and the table.
"Honestly, I was very happy to see the celebration because I was celebrating the goal on the bench. I think for Diego the most important thing was that he scored. The celebration was good, but most importantly he scored!"
Chelsea are now eight points clear at the top of the Premier League table with 16 games remaining, after Manchester City, Liverpool, Tottenham and Manchester United all dropped points.
Hull fought hard at Stamford Bridge, and could count themselves unlucky not to equalise. Conte insists every Premier League match is difficult.
"It is normal," added the Chelsea boss. "If you see the other games on this day, you understand that this league is very difficult. I continue to say that every game, it is not easy, every team and game is very tough, it is the reality.
"But we faced the game in the right way, and now it is important to continue and know that in every game, we must fight a lot to try to win and try to take the points.
"I think [we feel] both confidence and pressure. It is normal that now we are playing the second part of the season - only three games, we have 16 more games - that every game, three points become very big.
"But we are ready, we are ready to fight, face the opponent, and the games are very tough also for the other teams."
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