Conversion of outdoor area into building land - possibilities

I just checked the standard land values and on this map the eastern tip of the property is indeed not designated as a residential building area. That would at least fit the appraiser's assessment.

Nevertheless, I would simply try my luck with the approach proposed by Escroda.

Thank you very much for all your input and for taking the time for my concern.

I have now received a few answers from the district office. Unfortunately, completely excluding the topic of [Außenbereich] did not work. But basically, the caseworker does not consider construction to be ruled out, since there is already development to the north and south in this direction. He gave recommendations that the house should be positioned with its ridge direction running north - south, in order not to extend too far east with the construction. He also gave a few more tips and referred us to the person responsible at the city. To clarify whether construction is possible, we are to submit a preliminary inquiry.

Next, we will therefore seek a conversation with the person responsible at the city and hope to receive important tips for the preliminary inquiry or to clarify some questions (e.g., development) in advance.