After months of contract negotiations seemed to yield no agreement, Ramsey saw a final offer withdrawn by Arsenal and had been linked with both Liverpool and Chelsea when it became apparent that he would not be extending his stay in north London.
As such, Ramsey, who is eligible to formally sign a pre-contract with any foreign club in January when he enters the final six months of his Arsenal contract, has been tipped to sign a 'long-term' deal with Bayern that will begin at the start of next season.
It is expected to represent part of a wider 'refresh' of the Bayern squad after a poor start to this season has threatened the club's domestic dominance after winning the Bundesliga title by a minimum of 10 points in each of the last six seasons.
Borussia Dortmund lead the standings, with Bayern seven points off the pace in fifth place. The gap was extended when Bayern were beaten by Dortmund in Der Klassiker last weekend.
Bayern are no stranger to snapping up free agents. The Bavarian giants landed Leon Goretzka in the summer and famously paid nothing when they snatched Robert Lewandowski from Dortmund.
Assuming the report about his impending German adventure is accurate, 27-year-old Ramsey will tread a relatively untravelled path as a high profile British player moving overseas at the peak of his career. Similar examples are rare but include David Beckham, Michael Owen and Gareth Bale joining Real Madrid in 2003, 2004 and 2013 respectively.
A handful of British youngsters, including Oliver Burke, Ademola Lookman, Reece Oxford, Jadon Sancho and Reiss Nelson have played for German clubs in recent seasons.