Arsenal missed out on qualification for Europe's elite club competition for the first time in 20 years after finishing fifth in the Premier League last season.
Sanchez struck a career-best 24 league goals but increasingly cut a frustrated figure at the Emirates Stadium, especially as Arsenal were humiliated 10-2 by Bayern Munich in the Champions League.
And the 28-year-old Chile international, who has a year remaining on his Arsenal contract, declared his intentions for the first time in a television interview in his homeland.
"I want to play in the Champions League," Sanchez told Canal 13.
"The decision does not depend on me, I have to wait for Arsenal."
Arsene Wenger denied reports Sanchez has agreed a new contract when he spoke to the media on Saturday after Arsenal's pre-season win over Western Sydney Wanderers.
But the Frenchman is "positive" about talks with Sanchez, who is on holiday after featuring in Chile's run to the final of the Confederations Cup, where they were narrowly beaten by world champions Germany.
And prior to the game against Western Sydney Wanderers, Wenger confirmed that he had been in regular contact with Alexis regarding his future.
“I have spoken through text and it was very positive," Wenger told reporters.
“My thoughts are always positive. There’s not a lot to resolve at the moment with the player.”
Alexis netted 24 goals and added 10 assists for the Gunners last season before helping his country to the Confederations Cup final, and the Arsenal boss doesn't expect him back with the side until the end of the month.
“Players like Alexis Sanchez played the whole season, finished the season really tired and went off to play in the Confederations Cup," Wenger said.
“You can’t tell them they are not having a holiday and must come back and continue, it’s impossible.
“Usually you need three weeks but they will have a programme and can be involved after one week to ten days, and play a part in games.
“It also depends on the shape they come back in.”