Robben, 35, is approaching the end of his 10th and final season at the Allianz Arena, and Calciomercato.com (h/t Sports Illustrated) reported the veteran is more in favour of a switch to the United States.
His former Bayern team-mate Bastian Schweinsteiger has found success with Chicago Fire since joining the club in 2017.
The Nerazzurri may be disappointed to learn Robben would shun them for MLS, where the level of competition would be considerably lower. Sportswriter Nebojsa Markovic noted the havoc Robben could wreak if he was able to rediscover his old ways in North America's top competition:
Robben told reporters in December that this would be his last season with Die Roten, which came as little surprise given the recurring injuries that have restricted him to just 15 appearances in all competitions this season.
Five separate injury and illness absences have resulted in an underwhelming sendoff season for the player, per Transfermarkt. That's after the seven separate absences he endured in 2017-18.
Therein lies the concern in signing the 96-times capped former Netherlands international, as FOX pundit Alexi Lalas highlighted when Robben was linked with a similar move in 2018:
Despite making only 15 appearances this term, Robben has five goals and two assists to his name, equating to a little less than one direct goal involvement every other game.
The rigours of Major League Soccer might allow for the wizened winger to play under fewer pressures, but potential suitors may also expect their headline name to feature prominently.
Bayern's other stalwart wide man, Franck Ribery, is also expected to leave Bayern when his deal runs out in June, with young guns Kingsley Coman, 22, and Serge Gnabry, 23, expected to take over the reins.
In an ideal scenario, MLS would provide Robben with a stage on which to launch a late career revival, having carved out a reputation as one of the best to play his position, via BT Sport (UK only):
Bayern have travelled to the United States for pre-season contests in the past, but fans across the pond may look forward to getting a closer look at Robben's talents in the near future.