If implemented, that could put Washington at odds with close diplomatic partners with strict anti-gay laws, like Egypt, Saudi Arabia and Malaysia.
Grenell, the former US ambassador to Germany and openly gay himself, said he is conducting a review of possible options for action, which could include limiting intelligence sharing, according to the Times. Aid could also be leveraged to push countries to be more open to the LGBT community.
"We can't just simply make the moral argument and expect others to respond in kind, because telling others that it's the right thing to do doesn't always work," he told the newspaper in an interview.
"If a country that we worked in as the United States intelligence community was arresting women because of their gender, we would absolutely do something about it," he said. "Ultimately, the United States is safer when our partners respect basic human rights."