The Sun claims the Italian does not think the Brazilian, 24, works hard enough for the team and was lazy during the 3-2 loss to Real Madrid in Detroit on Saturday.
Asked if Oscar has a future at Chelsea, Conte refused to speak directly about the player, but did admit there would be departures from Stamford Bridge.
“All 29 players are Chelsea’s players at the moment. After this period I speak with my club,” he said.
“I agree after this tour to see all the players and then to take a decision. When we finish this period I will take the right decision for the player and for the club.
“There are players who will stay and others will go. This is football. It is important to be clear with all.
“My aim is to become a team on and off the pitch.
“To reach our target at the end of the season.
“My experience in my career as player and manager teaches me if you want to fight for the title you must be a team on and off the pitch. It’s very important.”
Inter and Juventus have been long-term admirers of the player, who rejected the chance to move to the Chinese Super League in January, although the Italian champions’ interest has waned to leave Roberto Mancini’s side as the frontrunners.