"Once that case is built and we have enough info to go on, then the arrest will be made and someone will be taken to trial in that case," he told KRBC reporter Jessica Reyes on Monday.
As leads continue to come in, investigators are trying to get all persons of interest cleared and narrow the case down to one person, he said.
Adkins was the last person to see Hailey before she vanished on Dec. 27. At the time, he was living with his girlfriend, Hailey's mom, but has since been staying in Dunn, Texas.
"As far as I know he is being watched some, but I cannot comment on (whether) he has been under 24-hour surveillance or not," Sheriff Toombs said.
Adkins has reportedly been traveling back and forth from Dunn to Big Spring recently.
"He's not under arrest, (so) his movements and what he's doing right now are his business," Colorado City police spokesman Pete Kampfer said.
Much of the investigation into Hailey Dunn's whereabouts has been happening around Texas and even out of state, with tips coming in from people who recognized Hailey from billboards or television.
"We have had possible sightings of Hailey in different places, so we do have to make sure we (...) verify with local agencies whether it was true or not," Toombs said. "That does take a little time."
The Colorado City Police Department, Mitchell County Sheriff's Office, Texas Rangers and FBI are still actively working the case.
They received much-needed assistance last ween from two private search organizations, KlaasKids and Laura Recovery Center, which trained local volunteers to be more efficient and effective.
Toombs said before the organizations left town, they put people in charge who will be leading another search later this week.