Sanchez, currently on international duty with Chile at the Confederations Cup, is about to enter the final year of his contract at the Emirates Stadium with no indication that he is ready to extend his stay in north London.
His contract situation, along with that of teammate Mesut Ozil, cast a shadow over a 2016-17 campaign which saw Arsenal finish outside the Champions League places for the first time in 21 years, a development which cast further doubt upon his future at the club.
German champions Bayern immediately emerged as a possible next destination for the former Barcelona forward, with Sanchez's compatriot Arturo Vidal keen to see his international teammate arrive at the Allianz Arena.
Bayern have already been busy this summer, looking to youth to strengthen Carlo Ancelotti's squad with the additions of Corentin Tolisso (22), Niklas Sule (21) and Serge Gnabry (21).
Speaking to Kicker, club president Uli Hoeness laid out Bayern's plans to continue building a side around youth, adding the club do not plan on spending big on older players – a category that would include 28-year-old Sanchez.
"Everyone is talking about building a new team and how Bayern Munich's future must be shaped," he said. "And then Bayern does exactly that, signs young players between 20 and 22, and is criticised once again.
"But you cannot build a new team with €100m transfers for 29 and 30-year-olds. That isn't a policy. Either we go down this road with all these young players, all getting a chance to play, or we don't go down this road."
Hoeness' comments would appear to hand an advantage to Manchester City. According to the Guardian, Arsenal's Premier League rivals are growing increasingly confident of signing Sanchez for a fee in the region of £50m, having been assured that the Chilean is keen to play under former manager Pep Guardiola once again.
It remains to be seen, however, whether Arsene Wenger would be prepared to sell his side's best player to a direct Premier League rival - even at the expense of losing him for free in 2018.