Bechtel, 25, has been missing since July 24, when she went jogging in the Loop Road area of the Shoshone National Forest.
Roger Rizor, an investigator for the Fremont County Sheriff's Department, said the search for the man began in mid-August when Bechtel's family told investigators about him. He said the FBI was looking for the man, whose name has not been released.
Rizor said the man is known to have been on the East Coast the night before Bechtel disappeared, which "almost eliminates him as a suspect," but said investigators still want to question him.
Rizor also said there were other people in Laramie who were "infatuated" with Bechtel while she was a student at the University of Wyoming. He said all those people have been contacted by authorities.