Employers are not required to interview an international student who has an F-1 or J-1 visa, even if the student is otherwise qualified for the job.
Some employers may have set policies stating that they will not sponsor, and therefore will not interview, F-1 and J-1 students, even though those students may have Optional Practical Training (for F-1s) or academic training (for J-1s) allowing them to work temporarily after graduation. This type of policy is lawful, and an employer can freely state that it will not interview or sponsor students in F-1 or J-1 status.
Can employers limit their interviewing/hiring to U.S. citizens?
Although employers can refuse to interview or hire international students who do not already have some form of permanent work authorization, most cannot stipulate that U.S. citizenship is a job requirement. (Note that "work authorization" and "citizenship" are different things. A person can be authorized to work in the United States without holding citizenship.)
As a general rule, an employer cannot legally limit job offers to "U.S. citizens only." An employer may require U.S. citizenship for a particular job only if U.S. citizenship is required to comply with a law, regulation, or executive order; is required by a federal, state, or local government contract; or the U.S. Attorney General determines that the citizenship requirement is essential for the employer to do business with an agency or department of the federal, state, or local government.
These exceptions are extremely limited in scope. An employer cannot simply impose a "citizens only" policy unless the job fits into one of the categories listed above. Even in those limited cases where "citizens only" may be allowed, the citizenship requirement must be related to a specific job that has been identified in the government contract, by law, or by the U.S. Attorney General. For example, an employer that is a U.S. Department of Defense contractor cannot require U.S. citizenship for all of its jobs relating to the contract if the contract identifies only certain jobs as requiring U.S. citizenship.
Accordingly, employers should not ask a job applicant about his or her citizenship during a job interview, unless the employer is confident that the job falls into one of the lawful bases for requiring U.S.-citizen applicants only. The employer, however, can ask if the candidate is authorized to work in the United States, and on what basis.