If the Gunners are to win their first league title since 2004, they need the Chilean to be focused after another Copa America victory.
Alexi Sanchez celebrates with the Copa America
Sanchez was voted player of the tournament, scoring three goals before Chile defeated Argentina on penalties in New Jersey.
There were similar high expectations last summer, when Chile also defeated Argentina in a tight Copa America final, with Sanchez starring in that tournament too.
The Gunners were full of optimism going into the season, with Sanchez's tournament-winning form and the signing of Petr Cech from Chelsea billed as the missing link in Arsene Wenger's side in order to put together a genuine shot at the title. But a surprise opening day defeat to West Ham saw that optimism checked, and Arsenal would only manage to win three of their opening six Premier League games.
Alexis Sanchez fights for the ball with Victor Wanyama
Chile star Sanchez started the derby against West Ham on the bench, coming on for the last quarter of the match, but he played from the off in the club's next five games, which included another defeat and a draw.
Crucially, the forward was unable to get on to the scoresheet until hitting a hat-trick in the win over eventual champions Leicester, which in turn started a run of goals for him and wins for the Londoners.
Soccer: 2016 Copa America Centenario-Argentina at Chile
With Sanchez likely to be arriving for pre-season training later than a lot of the Arsenal squad once more, and from further afield, there will be a worry that he will again start the season sluggishly.
Arsenal have a tough opening day match against Liverpool, and they will be conscious that an impressive start over the first few fixtures could get their campaign off to the kind of start necessary to make them title contenders.
Arsenal's Alexis Sanchez celebrates scoring