The Spain international played 29 times last season as the Blues regained the Premier League title, but only started on 13 occasions in the league.
Chelsea's return to European action means that Conte could find himself fielding two sides throughout the season: a core XI and second string.
Algeria international Mahrez has handed in a transfer request but is training with Leicester until a club matches their asking price.
Ronald McDonald made a surprise on-pitch appearance before Manchester United and Real Madrid kicked off their International Champions Cup match.
Jose Mourinho has challenged Anthony Martial to show more consistency for Manchester United ahead of the new season.
Manchester United manager Jose Mourinho is hopeful Ander Herrera's injury is not too serious despite lasting just six minutes against Real Madrid.