As an international student in Denmark, there are several options to consider for obtaining a work permit and potentially settling in the country. Here are some common paths:

1. Positive List and Pay Limit Scheme: Denmark has a Positive List and Pay Limit Scheme that allows skilled workers to obtain a work permit. If your occupation is on the Positive List, you can apply for a work permit without the need for a specific job offer. If your occupation is not on the Positive List, you can still apply if you have a job offer that meets the pay limit requirements.

2. Job Search Visa: If you have completed a higher education degree in Denmark, you can apply for a job search visa, which allows you to stay in Denmark for up to six months to search for employment. Once you find a job, you can apply for a work permit.

3. Start-up Visa: If you have an innovative business idea and wish to establish your own company in Denmark, you can apply for a start-up visa. This option is available for entrepreneurs who have a well-founded business plan and the potential for growth. Successful applicants receive a temporary residence permit to develop their start-up.

4. Family Reunification: If you have a spouse or partner who is a Danish citizen or holds a permanent residence permit in Denmark, you may be eligible to apply for a residence permit based on family reunification. This option allows you to join your family member in Denmark and potentially obtain a work permit.

5. Danish Green Card Scheme: The Danish Green Card Scheme is designed for highly skilled individuals who wish to work and settle in Denmark. If you meet the point-based system criteria, which consider factors such as education, work experience, language skills, and age, you can apply for a residence permit under this scheme.

6. Danish Citizenship: Obtaining Danish citizenship typically requires residing in Denmark for a certain period, usually nine years, fulfilling language and integration requirements, and meeting other specific criteria. The exact requirements may vary, so it's advisable to consult the Danish Immigration Service (Udlændinge- og Integrationsministeriet) for the most up-to-date information.