I’ve heard a few times that BMW is working on a 3 Series Gran Turismo, but a rumor floated at Germany’s Auto Motor and Sport claims the GT may instead be an all-new 4 Series.

If true, BMW Blog says that a 4 Series could be offered as a four-door coupe that would help BMW compete with offerings like the A5 Sportback.

The move would also enable BMW to offer a more stylish vehicle that slots well below the 6 Series in price while still demanding a premium over the 3 Series. And keep in mind that BMW has already green-lit the 6 Series Gran Coupe, which will feature two-door styling and four physical doors when it arrives in 2012.

Given that Audi has feverishly expanded its lineup the past few years, we wouldn’t blame BMW for countering with a 4 Series, but this is the first we’ve heard of it, so we’ll keep this one squarely in the rumormill category for now.