The 25-year-old has been widely expected to move to the Emirates this summer following claims that a £32m fee has been agreed with the Catalan giants.
While there has been no official announcement made by either club, Sanchez's hairdresser Carlos Moles appears to have quashed any doubt that the forward will not be an Arsenal player for the 2014-15 season.
A Facebook post by Moles has been translated as saying: "Alexis Sanchez said goodbye. Just as the newspaper Sport confirmed, Alexis Sanchez is leaving FC Barcelona to start a new phase of his career at Arsenal.
"During the three seasons that he was at Barca, the whole team at Carlosmoles salon, enjoyed having him."
Sanchez was also linked to Juventus and Liverpool, who are close to sanctioning the sale of Luis Suarez to Barcelona.