The agency's field office in Louisville has interviewed Heather Lowrey and conducted a background check.
The tweet, according to a screenshot provided to The Courier-Journal, says "If someone was cruel enough to assassinate MLK, maybe someone will be kind enough to assassinate Trump."
Special Agent Richard Ferretti said Tuesday that once the investigation concludes, the results will be sent to the US Attorney's office, which would decide on any potential charges.
Federal law prohibits threats to the president and the crime is punishable by at least one year in prison and a maximum of five years.