The Copa America winner could miss the Community Shield with Chelsea and the Premier League opener against West Ham.
The 26-year-old is not due back to first-team training until July 26 after Chile went all the way on home soil in the South American tournament, which is just a handful of days before the Gunners meet Chelsea in the Community Shield.
That match comes on August 2, meaning Sanchez would have had less than a week of pre-season training in which to prepare for the new season. And he may miss the London derby against West Ham that opens begins the Premier League campaign too.
The vast majority of the club's other players will return to training this week.
Arsene Wenger proved at the start of the season last year that he is willing to ease international players who had busy summers back into the Arsenal side, and the situation with the former Barcelona player will be similar to how the Frenchman dealt with the Gunners' German contingent after they lifted the World Cup.
None of Per Mertesacker, Mesut Ozil or Lukas Podolski featured in the Community Shield in 2014-15, or the opening Premier League game or first leg of the Champions League qualifier.
The latter is not a problem for Arsenal this season, but it may mean that a player who was arguably the club's best last season, may not be involved until the match away to Crystal Palace on August 16, and even if Sanchez is involved, it could be from the bench.