The agency says emergency crews responded to a report of a burning car in Dyersburg on Saturday and found the bodies inside the vehicle.
Wednesday, a family member of one of the victims identified one of the people in the car as 29-year-old Robert Williams.
Jennifer Williams said her brother was staying in Kentucky but has children in Dyersburg and Blytheville who he frequently visits.
The statement says the silver Ford Edge was a rental from Campbellsville, Kentucky and agents think the people inside are likely from there. Authorities think they traveled through Nashville to get to Dyersburg.
Authorities say it appears the occupants were a black male in his 20s and a white female in her 30s.
Anyone with information on their identities is urged to contact the bureau, which is investigating the deaths.
On Tuesday, Great River Road was covered in fog — much like the fog hanging over Saturday's grim discovery.
It made truck drivers like Dennis Walker wonder about the unknown. Walker drives by the area where the burned-out Ford Edge was found a few times a day, headed back and forth to the grainery not far away.
"That's bad stuff. I've never seen anything like that happen around here," he said. "It happened probably at night that is when no one is around."
Walker didn't notice the car until the sun came out. He also didn't know there were people inside.
"This truck driver has his own idea of what he thinks happened since learning the man and woman both aren't from the area and the rental car was registered out of Kentucky.
"It was supposed to be a drug deal," he speculated. "I guess they were trying to hide the evidence or something don't make sense."
Investigators haven’t said what the two were doing on the road about 15 minutes outside of the busier part of Dyersburg.
Right now they are just focused on figuring out the identities of the man and woman.
If anyone has any information call 1-800-TBI-FIND or Crime Stoppers at (731)-285-TIPS.