Sanchez's future at the Emirates Stadium remains uncertain, with his contract due to expire at the end of next season and talks over an extension reaching an impasse.
Speculation that the 28-year-old could look to leave the Gunners has increased since Arsenal's 5-1 defeat to Bayern Munich on Wednesday night, after which Sanchez was reportedly involved in a heated argument with teammates.
Chilean supporters have responded to his recent frustration by setting up a Facebook event with the title "National protest so that Alexis Sanchez leaves Arsenal".
The details of the march read: "We Chileans are tired of seeing one of our stars working by himself to make his team get through.
"We don't want him to play in Madrid, nor return to Barcelona, the truth is that that we don't give a damn what team he plays for, only that we want to see him fight along with 10 others to achieve results. Not on his own anymore."
Almost 15,000 fans have either said that they will attend the march or are interested in doing so.