To buy, no: the law requires no German bank account, and the price can come from abroad if paid by transfer and proven to the notary (§ 16a GwG). To own, you need an account, though not necessarily a German one: it receives the rent and pays the taxes, and in our experience a lending bank keeps the company's account in-house. An investor living outside the EU has no right to an account, and a bank may not accept deposits above €100,000 from Russian citizens and residents without EU, EEA or Swiss citizenship or a residence permit.
What to check:
• the price comes from your own account or the buying company's, and statements for every payment are ready by the due date;
• the source-of-funds documents for the full price are gathered before signing;
• the GmbH is entered in the Transparency Register before the account is opened;
• with a loan: where the bank requires the account and how the rent assignment is documented;
• for Russian citizens and residents: whether Art. 5b of Regulation No 833/2014 applies to you, or the exemption in its paragraph 3.