If you receive a residency permit without first having a job in Germany, the permit will explicitly forbid you from self-employment, eliminating the opportunity to work as a freelancer. As a contractor, the situation becomes less clear. If you secure some form of contract from a company outside Germany for regular freelance work, the German alien registration office may award you a work permit and residency permit. It’s difficult for them to discern between a contract for a full-time job from a foreign company and a contract for merely freelance work. The permit would be limited to that specific contract and would only be valid as long as the contract is valid. A German company would only be able to offer you contract work if they can prove no German can perform the tasks – and the job would be reflected in your residency permit. If you find yourself living off freelance income in Germany from jobs no German would be able to perform, you may have a case to win a work permit. Ask the Ausländerbehörde.