Diego Costa is ready to return to the Chelsea side and wants to stay at the club until the summer, Antonio Conte has insisted.

The Chelsea manager said Costa’s absence from the team last weekend was owing to a back injury and refused to even acknowledge the striker had been in conflict with the club over a multimillion-pound offer from a Chinese Super League club.

“Diego is available for the game against Hull,” he said on Friday. “He trained on Tuesday with the rest of the team and he trained very well. He has a good fitness. The pain in his back has gone, he has no pain in his back. For these reasons he is available for the game.”

Regarding Costa’s future, Conte said: “I think the player wants to stay at Chelsea. He is very happy to play with us and this idea [of a move to China] is far from his mind. He is happy to stay here, happy to play with us and this is the most important thing for us.”

Asked whether Chelsea might attempt to offer Costa a new contract, Conte replied: “It’s important to have the four months in a very strong way and then we’ll see. Now, it’s important to be focused on the present.”

Conte said he had yet to make a decision on whether to recall Costa to his starting XI for Sunday’s Premier League game at home to Hull. Chelsea eased to a 3-0 win over the champions Leicester City last week in Costa’s absence and Conte said he faced a difficult choice.

If he did select the striker Conte said he would be able to “put his hands in the fire”, an Italian phrase meaning he would be 100% sure of the player’s dedication.

“For me to make a decision is not easy”, he said. “I have four, five players who are very strong in that position – Willian, Pedro, Eden Hazard, Costa and Ruben Loftus-Cheek. They are in good form and they give me different options.

“For sure I sleep a few hours less to make the best decision but this is my task: to pick the best players game by game. For this reason it is important to know if one player stays out it is not for punishment. It is only because I like to make the choice game by game but also to consider the opponent.

“I think that every time Diego has played for Chelsea, he has always put all of himself out there for this club, for this shirt. For this reason I am sure that on Sunday if Diego starts the game he will put all of himself in the shirt for the fans and to win the game. I can put my hands in the fire.”

Conte also defended Jorge Mendes, Costa’s representative, who was recently photographed with the president of Tianjin Quanjian, the Chinese club believed to be behind the bid for the 28-year-old.

“I know Jorge and he’s a friend,” Conte said. “I have never heard Jorge talk about Diego or talk about a transfer for Diego. For this reason I think he has great respect for us and in this situation I think he acted with great respect.”

Conte said Chelsea were evaluating an offer, believed to be from Bournemouth, for their reserve goalkeeper Asmir Begovic.

“There is one offer,” the manager said. “It hasn’t been rejected – me and the club are trying to find the right solution. We are evaluating it but the club and the player both know my position. Asmir is a very important player for the club. He is an important player for me on and off the pitch and he knows this.”

The club captain, John Terry, is available to face Hull following his suspension after being sent off against Peterborough.