The 27-year-old Spain international has been linked with a return to former club Atletico Madrid after two seasons in England - the first of which saw Costa finish with a Premier League winners' medal.
But, despite sanctioning a deal to bring Belgium striker Michy Batshuayi to the club, Conte is determined to keep the Brazilian-born forward among his ranks for his debut campaign at the helm.
"Diego is our player," Conte said at a press conference in Austria, reported on www.chelseafc.com.
"He is a fantastic player, a player with a fundamental importance and there is no problem.
"He stays with us, he is working very hard, he is very happy to work with his team-mates and with me in the new idea of football
He is a Chelsea player.
"He is an important player, a very strong player, one of the best in the world, and I am sure when he goes into our ideas he will score a lot of goals for us."
Chelsea, who face WAC RZ Pellets in a friendly on Wednesday having lost their opening match under Conte to another Austrian side, Rapid Vienna, over the weekend, will again be without defender Kurt Zouma - even though he is making his way back to fitness after a serious knee injury
The France international underwent surgery in February after damaging his anterior cruciate ligament during the Premier League game against Manchester United
"Today he (Zouma) started the aerobic work for the first time," Conte said
But asked if the 21-year-old was involved, the Italian replied: "No
We wait because we must respect the right time for him.
" We know he is recovering but I know he needs more time to recover
It's important we don't push him
I had the same injury and I know from experience when the player is ready to go."
Source : PA
Source: PA