Ex-Croatian international Niko Kovac was sacked by Bayern after a string of poor results, culminating in a stunning 5-1 defeat to his former club Frankfurt on Saturday.
Wenger is set to be offered a short-term deal until the end of the season before Bayern decide on whether to offer him a longer contract, according to the Sun.
'Le Professeur' spent 22 years at Arsenal and has since spent over a year away from management.
Wenger has found a temporary home at beIN sports - as part of their punditry line-up.
The Frenchman denied currently being in discussions but maintained that he would "never refuse" talking to the German giants.
And conversations won't be an issue for Wenger, who is fluent in German - an added bonus for Bayern.
It's reported that full talks will have to wait until after Bayern's big clash with rivals Borussia Dortmund, when Wenger will meet with chairman Karl-Heinz Rummenigge.
Wenger had been offered a technical role at FIFA to help develop and improve education and coaching throughout the game.
However, such a proposal from Germany's most successful club is thought to push such a role onto the backburner for the time being.
Intriguingly, one of Wenger's first few games as Bayern coach could be a meeting with old foes Tottenham Hotspur, who were heavily beaten 7-2 by the Germans in October.
