The FDA said in a statement it could not comment on its discussions with companies, but added "we do generally work with sponsors to ensure the number of participants in clinical trials are of adequate size to detect safety signals".
The news was first reported by the New York Times.
US officials and independent medical experts said last month the benefits of the vaccines far outweigh the risks of the side effect, which has been reported in several hundred people younger than 30. But any vaccine safety issues could slow uptake, particularly among parents wary of taking any health risk with their children.
Currently, Pfizer has the only US vaccine authorised for children 12 years and up, while Moderna is expecting an FDA ruling on its application in the coming days.
While teens receive the same dose as adults, younger children may need smaller doses. That additional complexity adds time to drugmakers' research and application timelines.
Moderna said it expects to have enough data to apply for FDA authorisation in younger kids by late this year or early 2022.
Pfizer has previously said it expects to apply in September for children ages 5 through 11. Results for two younger age groups that began testing a little later should be available by October or November, according to the company.