No, it’s not a problem. The Green Card is all the proof you need of your status.

Yes big style!!
Renew your passport what’s the problem?

No, not if you already have the I-551 (green card). From what you said, you have a valid green card and a passport that is going to expire.

Two separate documents. Two separate uses. Two separate purposes.

Your green card is a document that takes the place of a an immigrant visa and can be used to show that you were granted permanent resident status in the U.S.

Your passport is a travel document issued by your country. It shows that you’re a citizen of Germany and identifies you.

It’s not a problem to have an expired passport until you want to travel. If you don’t go anywhere, it doesn’t matter. You don’t need a new stamp in the replacement passport when you get it.

The stamp was just temporary evidence that you qualified for a greeen card. Now you can use your green card.

No problem. My neighbor has had a green card for 20 years and doesn’t have a passport. You will need a passport if you plan to leave the country.

It’s a problem if you don’t have your German passport and you’re going to travel out of the country.

What do you mean the new passport won’t have the stamp? what stamp?.

If you really have a greencard, you don’t need any stamp in your passport.
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It is no problem. As long as you have your green card you will be fine.