Sources told ESPN FC on Friday that Costa had trained alone at Cobham for three days and been dropped from Conte's squad for the Leicester City match after a heated argument with a fitness coach over an injury and a lucrative offer from a Chinese Super League club to sign him in January.

A double from Marcos Alonso and a goal from Pedro Rodriguez ensured Costa was not missed at the King Power Stadium, hours after sources close to the 28-year-old had told ESPN Brasil that he is not interested in moving to China this month, but his absence still dominated Conte's post-match media duties.

"If you want to know the truth, I'm ready to tell the truth," Conte said. "The truth is this: 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 and for this reason today he wasn't available to come with the squad. This is the reason, this is the truth."

Asked if Costa had argued with a fitness coach, Conte added: "I read a lot of speculation about this topic. I can say that if -- I repeat, if -- there are problems with players, I'm used in my career to solve the problem in the changing room, not outside or in a news conference. I told you the truth."

On the subject of a possible bid from China, he insisted: "I don't know anything about this. The club didn't tell me about this. For this reason it can be only speculation."

Conte, however, refused to confirm whether Costa has a future at Chelsea.

"Today I can't be concerned about this because my players showed me a great performance, great spirit of a team and it's very important," he said.

"When you are able to win this type of game, a tough game 3-0 against Leicester who last season was champions and this season is improved [as a team], I can't be concerned about anything. I must be pleased with my players, to work with them and to continue to work with them."

Pressed on whether Costa still has a chance to play at Chelsea again, Conte replied: "Why not?"

Conte also said he does not know the extent of Costa's back injury.

"I don't know," he said. "It's always difficult because the pain I don't have, his pain. It's important to understand when he recovers. We'll see next week about this."

Chelsea's win puts them seven points clear of second-placed Tottenham -- though Liverpool will have the chance to narrow the gap to five when they take on Manchester United at Old Trafford on Sunday -- and Conte is pleased that his team has put the pressure back on their rivals.

"Now we've started the second part of the season, and the points are very heavy for all the teams," Conte added. "Now we stay on top of the table and if you win you put pressure on the other teams.

"We started this game with great pressure after Tottenham's victory, after Arsenal's victory, and we had to show good experience to manage this situation."

Leicester's defence of their Premier League crown continues to be a struggle and defeat leaves them five points above the bottom three.

But boss Claudio Ranieri insists his players have the stomach for a relegation battle.

"From the beginning we have been looking over our shoulder but we are in good condition and I am sure now we can get some more points," he said.

"The mentality is right, we fight. This team is used to fighting. Three seasons ago they fight to win the Championship, two seasons ago they were battling against relegation and in the end they survived and last season they won the title. These players know how to fight."