The eligiblity criteria for getting private health insurance depends mainly on your occupation. Employees are eligible for private health insurance if they meet the annual gross income limit (JAEG).
Civil servants can be insured privately without any prerequisites and level of income. In the majority of cases the employer covers half or more of the insurance cost similar to employees.
Self-employed, freelancers and students can freely choose to be insured privately. Addidiotnally, public health insurance providers are not obligated to cover third-country nationals so in many cases self-employed persons need to take out a private health insurance.