Costa is available for selection again after missing Chelsea's trip to Leicester City with what Conte insists was solely a back injury, though sources told ESPN FC last Friday that the 28-year-old had also been sent to train alone for three days and dropped following a training ground row with a fitness coach and a lucrative offer from Chinese Super League club Tianjin Quanjian.

Chelsea won 3-0 without Costa at the King Power Stadium and the striker trained alone at Cobham on Sunday and Monday before rejoining the rest of the squad -- who had been granted two days off after the victory -- on Tuesday.

Conte is adamant that Costa is fully focused on maintaining Chelsea's challenge for the Premier League title, and says he does not expect fans to turn against him in the way they did following Jose Mourinho's sacking in December 2015.

"Every time Diego played for Chelsea, he always put all himself into it for this shirt, for this club," Conte said of Costa. "This is the most important thing. I know this and I'm pleased for this.

"For this reason, I'm sure on Sunday that, if Diego starts the game, he'll put all himself into it for this club, the shirt and the fans, and do everything he can to win the game.

"I don't think this situation can happen [with fans booing him]. It's not right, it's not right. I repeat: Last week, he had this injury, this pain in his back. Now he came back with us. I'm sure that, together, we have to win against Hull City. It's important for me to be focused on all: on me, on the players, on the fans and on the game, because it's a really important game for us to win.

"Our fans are really important, always, because they are great. They push a lot when we play at home. They push a lot when we play away. And, for us, for me, they are the 12th player on the pitch. I hope to continue in this way, to push a lot our team, my players, in every moment of the game. They are a really important part for us to try and win and try and continue to fight for the title."

Chelsea's form in the Premier League without Costa this season -- 3-0 wins over Bournemouth and Leicester City -- means it is far from certain whether the Spain international will even make an instant return to the starting XI, and Conte says he does not want any of his players to feel that their places are safe.

"I must be honest, I don't like this word, 'untouchable,'" Conte admitted. "You prove you should play a game in training sessions, and you have to prove you should start. I don't like this word, this adjective, 'untouchable.' I prefer all my players show me every single day that they deserve to play on Sunday. For me, that's important. From my career, I learnt this."

Asked if Costa will be mentally ready to play if called upon, Conte replied: "Yes. I can put my hands in the fire. In Italy, if you put your hands in the fire, it means you are certain 100 percent. It means you trust 100 percent the situation."