Following reports this week that Costa had a disagreement with the Chelsea boss and his coaching staff amid rumours of a big-money offer from a Chinese Super League club, the 28-year-old was left out of the squad on Saturday evening.
Conte played down his top scorer's omission before kick-off at the King Power Stadium, saying he had a back injury, and he insisted that was the truth in his post-match press conference, where he also called talk of an offer from China "speculation"
Asked if Costa still had a future at Chelsea, Conte replied: "Why not?
"This is the truth
O n Tuesday Diego stopped training because he felt a pain in his back and from that moment he doesn't train again this week
And for this reason today he wasn't available - for the starting XI or the bench or the squad
This is the reason, this is the truth
"I think there has been a lot of speculation about this topic
If there is a problem, and I repeat if, with the players then in my career I prefer to sort the problem in the changing room, not outside and not in press conference
But I repeat - if
I have told the truth."
Earlier this month Costa was linked with a move to the Chinese Super League, with the accompanying astronomical wages
It was rumoured Tianjin Quanjian were prepared to bid Â£80million for the Spain international
" I don't know anything about this
The club don't talk to me about this so it can be only speculation," Conte added
Costa has been prolific this season for a Chelsea side now seven points clear at the top of the Premier League after Saturday's 3-0 win against Leicester, scoring 14 goals in 19 Premier League games
Chelsea coped well without their talisman at the King Power Stadium thanks to two goals from Marcos Alonso and another from Pedro but they will not want to be without Costa for too long
Asked when the striker might be fit again Conte remained coy, instead preferring to praise his other players for their performance and victory
"I don't know when he will be fit
I don't have the injury or the pain
We will see next week," said the Italian
" It is important to understand his physical condition and then we see if he starts to train
"But I think we are talking about this topic a lot and it is a bit of a lack of respect for my other players for their performance
I have replied in all ways and trust me this is the truth
For me, I don't like to answer this type of question - ''if''
"Today I can't be concerned about this because my players showed me with the performance great spirit and it is very import ant when you are able to win this type of game - against Leicester last season who were champions - and when you win 3-0 it means I can't be concerned and I must be pleased for my players
"We must be pleased because it is important to talk today about the players who played this game
I am pleased because after 10 wins in a row and then a defeat it is very difficult to know the reaction but our reaction was very good and I am pleased for this and I want to thank my players, who wanted to fight and wanted to win."
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."
Source : PA