Spanish newspaper Mundo Deportivo claim the the 27-year-old striker is keen to push through a return to former club Atletico Madrid this summer.
Costa hit the ground running in his debut season at Stamford Bridge – scoring 20 goals to clinch the 2014/15 Premier League title – but struggled last term as the Blues slumped to a 10th-place finish.
Recent reports have suggested the Brazil-born Spain international has handed in a transfer request, but Conte insists he remains happy at the west London club.
“Diego Costa is our player, he’s a fantastic player with fundamental importance. He’s very happy and is working hard,” he said.
“I’m very happy with our work, I found the players have the right attitude and they are great workers. I’m seeing a great attitude and great behaviour from the players and we must continue that for the whole season.”
Conte officially took charge at Chelsea earlier this month and has wasted no time in the transfer window, signing striker Michy Batshuayi and midfielder N’Golo Kante.