The 35-year-old is currently available on a free transfer, having left Lyon when his contract expired in June.
Boateng previously represented the Munich giants between 2011 and 2021, making 364 appearances in all competitions, winning nine Bundesliga titles, five German Cups and two Champions League crowns.
The German only made 35 appearances during his time at Lyon due to fitness problems, but he is now back training with Bayern and could potentially earn himself a short-term deal at Allianz Arena.
A statement from Bayern on Sunday morning confirmed that their former defender was part of the club's first-team training session following the clash with RB Leipzig on Saturday.
"Following Bayern's 2-2 draw away at RB Leipzig in the Bundesliga on Saturday, the players who didn't start the game completed a training session at Sabener Strasse on Sunday," read the statement.
"Among those involved was two-time treble winner Jerome Boateng. The 35-year-old defender is currently without a club following the expiration of his contract at Lyon.
"The 2014 World Cup winner lifted the Champions League twice during his previous stint at Bayern, as well as the Bundesliga nine times, five DFB Cups and Supercups each, and the Club World Cup twice.
"Boateng was named Germany's Footballer of the Year in 2016 and will continue to train at Sabener Strasse over the coming days."
According to German journalist Florian Plettenberg, senior figures at Bayern are willing to offer the central defender a short-term contract.
Plettenberg claims that discussions are currently taking place between the two parties with the view to coming to an agreement over a deal.
Bayern are said to be aware that there will be opposition to the move, but the club are confident that he would strengthen a squad which is looking to challenge on all fronts this season.
The Munich outfit's head coach Thomas Tuchel is said to be an admirer of the German, allegedly attempting to bring him to Paris Saint-Germain when he was in charge of the French club.
Bayern are currently preparing for their second match in the group stage of the 2023-24 Champions League, facing a trip to Denmark to take on Copenhagen.