The idea is not that he'll be turning up in America any time soon - his contract with Bayern Munich does not expire until 2016 - but that the sun is setting on his career at the only club he has played for (unless count Bayern's reserve team as a separate entity) as a professional footballer.
Contract renewal talks were reportedly scheduled around the 2014 World Cup, but suspended and have yet to be resumed. Further, there is the fact that Schweinsteiger has made just 15 league appearances for Bayern this season. Even if he plays in each of the club's remaining five Bundesliga matches, he will have made his fewest league appearances for the first team since his debut season, 2002-03.
In part, this is simply because of injuries, but there is a perception in some corners of the German media that Pep Guardiola may increasingly be sold on Xabi Alonso, Philipp Lahm, and Thiago Alcantara to do the sort of midfield work Schweinsteiger has been doing very well for more than a decade.
Throw in the fact that Bastian will turn 31 this summer, and that Bayern will have to bring forward a younger generation over the next few years, and one has the makings of a transfer rumor: a player the wrong side of 30, with an expiring contract, diminishing first-team playing time, and an apparently uncertain place in the starting lineup - that sounds a lot like a player on the outs.
Dietmar Hamann doesn't even think Schweinsteiger will be playing for Bayern next year. (One should point out Hamann also wrote off Bayern's chances of making it past Porto in the Champions League this year.)
On the other hand, there is the fact that Schweinsteiger does still have a year to run on his contract. A year in which, as captain of the German national team, he may yet lead his country to the 2016 European Championship. And he may still have a part to play in Bayern's ongoing Champions League campaign this year, as well as having a full season to work his way back into Guardiola's good books in 2015-16.
Sport 1 also points out that Schweinsteiger's agent is keen to see contract talks resumed, which is presumably the primary spur for the emergence of this timely reminder to Bayern's front office that their stalwart midfielder is not without options.
All told, the German press is inclined to cling to Schweinsteiger's January comment that he expected to play "at the highest level" for another three or four years as evidence against a move to a destination as lowly as MLS. Sportal rather dismissively rates the chance of the captain of the reigning World Cup holders moving to the US at 20%.
But Sport 1 also notes that the Bayern Munich lifer has said some nice things about America in the past - and about New York in particular. And back in February, the LA Times quoted Schweinsteiger making polite noises about MLS:
"We will see what happens in the future. But to be honest, I like the States."
Far-fetched speculation? Surely. But the whispers will only proliferate as long as Schweinsteiger languishes on his current, expiring contract. Indeed, Turkish outlet Haberciniz is already declaring the usual MLS suspects - Orlando City and NYC FC - to be among the clubs chasing his signature. And RBNY.
That's the Red Bulls twice linked to a player just making his first tentative steps on to the rumor mill. We're watching you, Bastian. And just maybe, he's watching us.