Costa is poised to return to Conte's team for the clash at Stamford Bridge after being dropped for the win at Leicester last week following a training-ground bust-up between the striker, the manager and Chelsea's fitness staff.
That occurred with the backdrop of an extraordinary £30million-a-year offer to the striker from Chinese Super League club Tianjin Quanjian.
Costa, who had complained of a back injury, trained on his own on Sunday and Monday but for the rest of the week worked with the squad and is now set to make his 100th appearance for Chelsea.
Antonio Conte insists he trusts Diego Costa despite and has begged the fans to have faith in him
"Diego's focus and concentration is at the level I want. He is mentally ready to play," said Conte.
"I can put my hands in the fire. What does it mean? In Italy, if you put your hands in the fire, it means you are certain 100 per cent. I means you trust the situation 100 per cent.
"If Diego is not concentrated and starts the game, the fault is mine. Because I didn't see it. I made my choice, and it would have been a bad choice.
"It wouldn't be the player's fault, it would be mine because this week, I didn't see that he wasn't focused or concentrating and was thinking about other situations."
Costa all smiles after returning to Chelsea training ahead of their clash against Hull
Conte insisted that the offer from China – now apparently withdrawn because Chelsea will not sell in January – will not affect Costa.
"Every time Diego has played for Chelsea, he always put all of himself into it – for this shirt, for this club," said the manager.
"I'm sure that, if Diego starts, he will put all of himself into it for this club, the shirt and the fans, and do everything he can to win."
And Conte believes the fans will back Costa and not boo their leading scorer, even though he is now certain to leave at the end of this season and will not sign a new deal, as Express Sport revealed this week.
The Italian said: "I don't think this can happen. It's not right.
Conte insisted that he does not want to sell Asmir Begovic to Bournemouth
Chelsea train ahead of Hull clash
Fri, January 20, 2017
Express Sport brings you all the best snaps as Chelsea train ahead of their clash with Hull on Sunday
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Diego Costa was all smiles as Chelsea train before their clash with Hull
"Last week, he had this injury. Now he is back. Together, we have to win. It's important for everyone to be focused: me, the players, the fans, because it's a really important game.
"Our fans are always important, they are great. They push us at home and away. For me, they are the 12th player."
Conte, whose team go into the weekend with a seven-point lead, added: "Diego is happy to stay. It would be a great achievement for him, his 100th appearance. I hope to celebrate that with a win."
Conte admitted Chelsea were considering an £8m offer from Bournemouth for second string goalkeeper Asmir Begovic but he does not want to sell.
"We are evaluating this," he said. "But the club and the player know my position. For me, Asmir is a really, good important player."