According to two US officials cited in the report, two or three people on board are believed to have been killed.
If confirmed, the strike marks the eighth US strike against suspected drug boats since 2 September - but the first in the Caribbean.
The BBC has contacted the White House, Pentagon and State Department for comment.
In a leaked memo recently sent to US lawmakers, the Trump administration said it determined it was involved in a “non-international armed conflict” with drug-trafficking organisations.
At least 34 people have been killed in the American strikes on alleged drug boats, including a recent strike on a semi-submersible vessel in the Caribbean.



What? When has Al Qaeda attacked the US homeland since 9/11?