The 69-year-old is ready to return to football after leaving Arsenal in May.
Reports claim he snubbed the chance to replace sacked Slavisa Jokanovic at Fulham earlier this month.
However, Wenger has no intention of taking over another English side after 22 years in charge of the Gunners.
But the Frenchman does fancy a move to Germany to take up the reins at Bayern, says the Daily Telegraph.
The Bundesliga champions have struggled this term under Niko Kovac.
And just two wins in their last eight league games has seen them fall nine points behind leaders Borussia Dortmund.
Bayern and Kovac suffered their latest setback at the weekend, blowing a 3-1 lead to draw with strugglers Fortuna Dusseldorf.
And reports in Bavaria claim Wenger's name has been mentioned by the club’s top brass as a potential replacement for the hapless Kovac if he gets his marching orders.
Wenger has declared in recent interviews he could be back at work in the New Year.
The experienced French coach who is fluent in German would jump at the chance to end his career competing for trophies at the top level in one of Europe's elite leagues again.
Wenger has not been short of offers since the summer after being linked with the technical director job at Paris Saint-Germain.
He described reports of replacing Gennaro Gattuso at AC Milan to reunite with ex-Arsenal chief Ivan Gazidis in Italy as “fake news”.
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