The German champions have decided they need to strengthen their attack and believe "it is quite possible that coach Arsene Wenger would let one leave," per Bild (h/t Sport Witness).
The report also noted that both players would be available to play in the Champions League for Bayern, as Arsenal failed to qualify for the competition after finishing fifth last season.
Striker Lacazette is Arsenal's record signing and only arrived in the summer from Lyon. Opta noted how he has made an instant impact:
Bayern may be interested in Lacazette, but trying to sign a player that Arsenal only spent a club-record fee on in July looks all but impossible.
Welbeck, meanwhile, has endured an injury-ravaged time at Arsenal and is currently sidelined again with a hamstring problem.
He is not expected back until after the international break, per injury data analyst Ben Dinnery:
However, he had started the season in good form with three goals and an assist in six Premier League starts, per WhoScored.com.
Arsenal may also be loath to allow any of their attacking players to leave, due to the continued uncertainty over the futures of Alexis Sanchez and Mesut Ozil.
The duo are out of contract in the summer, and Wenger has said that both players could leave in January, per John Cross at the Mirror.
Striker Robert Lewandowski, meanwhile, continues to shine for Bayern and is certainly delivering the goods again this season, per Squawka Football:
Any striker who does come in will very much be playing back-up to the prolific 29-year-old, a role that will surely not appeal to Welbeck, particularly as he has missed so much football due to injury.