Bayern CEO Karl-Heinz Rummenigge said it is not a problem for Bayern as their key concern is to find back-up for Robert Lewandowski, and Sanchez is not a genuine No. 9, per Sky Germany (via Simon Bajkowski of the Manchester Evening News): "I think Sanchez has already decided which club [to join], so I suppose that the door will be closed in January. That’s not an issue, and he is no direct substitute for Robert Lewandowski as he is not a real centre forward."
Chilean Sanchez, 28, is out of contract with Arsenal at the end of the season and likely to be available for free.
It remains unlikely he will pen new terms at the Emirates Stadium, but Arsenal manager Arsene Wenger recently indicated he expects Sanchez to remain past January despite ongoing links with Manchester City, per The Guardian's David Hytner.
The Sky Blues offered Arsenal £60 million for the former Barcelona forward on deadline day of the summer transfer window, but the move collapsed when the Gunners failed to sign Thomas Lemar from Monaco as his replacement, per Hytner.
It is likely Sanchez's departure from Arsenal was merely delayed.
But Bayern seem to have fallen out of the race to snap him up despite looking set to be the favourites to sign the Chile international at one point late last season, per Sam Wallace and Jason Burt in The Telegraph.
Sanchez's form could potentially be another reason the German giants have cooled on him, as he has netted just once in eight league appearances so far this term, per WhoScored.com.
Bayern need to add more firepower to their ranks as they remain overly reliant on Lewandowski to find the net. He has top-scored for the club this season in the Bundesliga with 11 goals, while Arjen Robben is the second-most prolific with three.
Conversely, Pep Guardiola's City, who now look front-runners to eventually sign Sanchez, arguably have little need for the Chilean, as they already have four players with more than five league goals in 11 matches this term—Sergio Aguero, Leroy Sane, Raheem Sterling and Gabriel Jesus.