Costa has not been to Chelsea's Cobham training ground since the end of last season and has been posting pictures on Instagram from his hometown of Lagarto in Brazil just days before the new season begins.
However, the failure to secure reported transfer targets such as Romelu Lukaku and Leonardo Bonucci, Diego Costa's pariah status and the departure of Nemanja Matic to the benefit of Manchester United all appear to have irked the former Juventus boss.
Costa has been Chelsea's top scorer in each of his three seasons with the Blues, including two title wins, and remains at the club, with Atletico Madrid's interest in re-signing the striker complicated by their transfer ban.
Conte and Chelsea are adamant Costa was aware of the situation in January. He is a great friend who is unfortunately no longer with us.
Chelsea have spent close to £130m for the likes of Morata, Antonio Rudiger, Tiemoue Bakayoko and Willy Caballero but that might not be enough.
"It won't be easy to repeat an awesome season like previous year", he said.
Speaking at a news conference ahead of the clash with Sean Dyche's side, Conte played down his team's prospects of becoming the first club to defend their title since Manchester United in 2008-09. He will need to get used to the Premier League but then he will perform.
Asked if he would start against Burnley on Saturday, Conte said: "He's working very well and starting to understand our idea of football". "I like him and I hope it works out". The transfer market is not finished. We want to be competitive and we want to try to fight this season for the title.
"I think this is a great possibility for Michy", Conte said in a press conference on Friday. Me and the other players are here to give all the support to our new players, for they can earn at Chelsea what they have been doing in their previous clubs.
"Alvaro is a really good player, he's still young despite having a lot of experience", Conte added.