Speaking about when the Chilean will be ready to return to action after a hectic summer, Arsene Wenger revealed he only expects him to miss the Premier League opener against London rivals West Ham on August 9th, as reported by the Guardian.
The match is Bilic's first league game in charge of the Hammers and the Croatian will be looking to make an instant impact on his return to England as a manager.
Sanchez has spent his summer helping Chile to a first Copa América title in 99 years, off the back of a starring role in the Gunners' emphatic FA Cup final victory over Aston Villa.
But Wenger has confirmed he will be without his star man as the North Londoners aim to start the season in a positive manner in a bif to challenge for the title.
“Alexis will be back on August 3rd," Wenger told the Guardian.
"Usually it takes three weeks to be competitive. With Alexis it could be a bit less. He will miss certainly the first game.
“He is an important player for us and he showed he has the winning mentality when he took on the responsibility to take the last penalty in the Copa América final against Argentina.”
Why Bilic will be relieved at Sanchez absence
That winning mentality and Sanchez's potency - he scored a goal every other game for the Gunners last season - are exactly why Bilic will be glad he isn't facing him on his Premier League managerial debut.
While Arsenal have a squad brimming with enough quality to cope in the brilliant Chilean's absence, West Ham have been one of the busiest clubs in the transfer market this summer and will be no pushovers.
Sanchez's influence cannot be underestimated.
At the halfway stage last season, statisticians worked out that Arsenal would have been 14th in the Premier League without their star man, as reported by the Telegraph at the time.
At that point, the former Barcelona man had scored 14 goals in 18 games for the club he joined for £30 million last summer, including nine in the Premier League.
The second half of the season wasn't much different either as he completed one of the most dazzling debut seasons of the Premier League era.