Does a German citizen living in the US and visiting Germany need to be concerned about re-entering the US when the German passport expires within 2 months, or is a valid Green Card all that matters? Are there any other concerns to be aware of? Should the person carry a statement from the German Consulate that a new passport is in the process of being issued?
To return to the USA, you need only the green card. A passport is not required - at least the USA does not require it, and Timatic (the database which airlines use to verify passenger travel documents) makes it clear that green card holders don't need a passport to enter the USA, so the airline should not ask for one. But watch out for new check-in agents who don't understand Timatic, and overly strict airlines with company policies requiring a passport even when the government does not.
Also, depending on your itinerary, other countries that you transit might require a valid passport. That probably isn't going to be an issue if you just fly from the Schengen area to the USA though.