The Arsenal forward has been strongly linked with a move away from the Emirates this summer – and Bayern are one of the teams sniffing round.
Sanchez has grown increasingly frustrated with Arsenal following a disappointing second half to the campaign, which saw them finish outside of the top four for the first time since Arsene Wenger took charge.
He will spend the summer in Russia with his international team-mates with Chile set to play in the Confederations Cup.
But the gaffe came as the nation’s football association released their squad list on Twitter.
Sanchez’s name was listed next to the Bayern badge.
Chile’s Arturo Vidal admitted earlier this week that he has been asked by Bayern about Sanchez with the view to a summer transfer.
Vidal has been named in the Chile squad for this summer’s competition, which runs between Saturday 17 June and Sunday 2 July.
“Bayern have asked me about Alexis and I’ve always told them that he is the player who should come here,” Vidal told Spanish newspaper Sport .
“I would like Alexis at Bayern. He is doing well at Arsenal but I think he has to take a step up and fight with the best in the world.”
Sanchez should, however, play at least one more game for Arsenal, with the FA Cup final taking place on Saturday afternoon.
The Gunners take on Chelsea in a bid to end their disappointing campaign on a high – and with a trophy.