Yes, it is possible to apply for a green card while on an F-1 student visa, but you must be eligible under a qualifying category such as family-based sponsorship, employment-based sponsorship, or other immigration programs. Keep in mind that the F-1 visa is a non-immigrant visa, so you must avoid actions that contradict your temporary intent until your green card petition is properly filed and accepted.

While holding a student visa, you may pursue a green card if your circumstances change and you meet the eligibility requirements. Since F-1 visas do not permit dual intent, applying for a green card must be based on a lawful route such as through a family relationship, employment opportunity, or other qualifying basis.