The investigation, reports the El Paso Times, was sought by U.S. Rep. Silvestre Reyes, D-Texas, who said in a letter to the agency, "It is my understanding that the threats were made by members of a drug-trafficking gang in Mexico."
An FBI spokeswoman in El Paso said her agency has not yet started an investigation, but did not rule it out.
The threats reportedly came after a Jan. 23 standoff when deputies pursued drug smugglers to the U.S.- Mexico border near Sierra Blanca, the newspaper reported. The suspects were then joined by armed men in military-style clothing and crossed into Mexico.
Mexican officials have denied the involvement of their military.