BMW is building a mid-size Gran Turismo, with the form factor something along the lines of a smaller 5-Series GT, that much we know. Whether it will be called the 3-Series GT or come as a new model, a possible 4-Series, remains unclear. But whatever it's called, this is what it will look like.
Or at least, this is most of what it will look like. These spy shots are the most recent of the upcoming long sedan/not-quite-a-hatch/don't-dare-call-it-a-wagon from BMW. It is almost certainly riding on the platform under the new 2012 BMW 3-Series and powered by the same slate of engines as well, meaning a duo of naturally aspirated and turbocharged four- and six-cylinder units. BMW is also working on a new family of three-cylinder engines, but their appearance in the 3-Series line is not expected for several years.
Don't expect the new 3-Series Gran Turismo until sometime in late 2012 or early 2013, despite a 2009 prediction of a 2011 launch for the car by CEO Norbert Reithofer. Perhaps you shouldn't be too eager to see this car in the U.S. at all--at least not if you're a wagon-lover, as the 3-Series GT is likely to displace the 3-Series wagon in the U.S. just as the 5er did for its cousin.
Interestingly, BMW is also rumored to be working on a smaller 1-Series Gran Turismo