The Bundeswehr has to make do without cheap short-service conscripts soon and is about to finally re-think its approach to recruitment.
The typical fear is that recruitment enough good young men will be difficult ( = expensive). This isn't surprising, for the Bundeswehr never felt the need to become good at recruiting!
One of the proposals for this issue caught the attention of mainstream media; the proposal to regularly recruit minorities living in Germany without a German citizenship.
To be honest, I doubt that this would be a major relief, and a few per cent foreign volunteers in the army couldn't justify much fear about their loyalty. It's likely not going to help the combat troops cohesion, though.
Nobody seems to intend to hire foreign nationals as officers or for some kind of almost entirely foreign-manned Légion étrangère anyway.
I served with a native Indian and some native Russians in my unit back in the 90's; foreign looks and foreign behaviour patterns are no real news to the Bundeswehr. A passport is just a piece of paper and doesn't change much if the person was raised here and has lived here for many years. I expect that many minority guys serving voluntarily and gladly in the Bundeswehr would easily exceed the loyalty and determination of many if not most German 1990's peacetime conscripts.
In the end, it's a question of junior leadership (in the platoon) and comradeship among the troops how well such few per cent foreign nationals would serve in the army. This is probably the real problem; the Bundeswehr has deteriorated in these areas after the Cold War.
P.S.: It's unlikely to happen if there's significant publicized opposition to the idea. The Minister of Defence von Guttenberg is not someone who puts up a fight for such detail ideas. He's rather the kind of politician who tests reactions by asking for proposals and allowing them to become publicly known to test them before he commits himself to a plan..