49 CFR §1552.35

1. (a)A candidate may be eligible to participate in flight training if the candidate—
   1. (1)Is lawfully admitted to the United States, or entered the United States and has been granted permission to stay by the U.S. Government, or is otherwise authorized to be employed in the United States; and
   2. (2)Is within their period of authorized stay in the United States.
2. (b)A candidate who has yet to obtain a valid document issued by the United States evidencing eligibility to take flight training may be issued a preliminary Determination of Eligibility pending the individual's ability to provide proof of eligibility.
3. (c)A candidate who engages in a flight training event that takes place entirely outside the United States is not required to provide eligibility for flight training in the United States, but must provide any United States visas held by the candidate.
4. (d)Any history of denial of a United States visa may be a factor in determining whether a candidate is eligible to participate in flight training, regardless of training location.