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.
Bayern find themselves fourth in the Bundesliga and see the 70-year-old as the perfect man to navigate the champions back to the summit.
'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.
It was on their show yesterday, whilst covering Champions League action, that Wenger refused to rule out taking the Bayern job.
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.
Then there is an international break in which to potentially thrash out a deal that could see the veteran coach make the move to Bavaria.
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.
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