It is most likely a larger size shawm. Bass and larger 16th C recorders usually had a removable cap, often with a brass band on the end, similar to the ones on the fontanelle (the "pepper-pot" covering the little finger key). You would see this even if the instrument were turned so that the window was facing away from you. The edge between the side and the top of the cap was typically beveled. You don't see any of this in the painting. Also, the instrument in the painting is a bit slender looking for a recorder of that size, but not for a shawm. Compare the painting with the Praetorius woodcuts. (Without getting into the theorbo debate, the woodcuts correlate pretty well with surviving instruments for the woodwinds.)
...Bob I'd guess a great bass recorder, especially since there are other recorders in the pictures. It's not a bassoon or dulcian. Those have a U-shaped structure, and this looks like a single bore instrument. FWIW, the only extended tenor shawms I've seen (one of them in our loud band) use a slightly bent bocal, not the bassoon-like one in the picture, and the top of the instrument is not nearly as broad, but there could be other designs I'm not aware of. -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html