A police spokesman would not say how investigators believe Lopez-Buelna was connected with the kidnapping case or explain the delay in reporting Lopez-Buelna's arrest on a charge of possession of firearm by a prohibited person.
Lopez-Buelna was due to appear before a judge in Las Vegas on Wednesday.
Officer Cris Johnson, a police spokesman, said he didn't know if Lopez-Buelna had a lawyer.
Lopez-Buelna is the fourth person of interest named by police since Cole was snatched from his home Oct. 15 by two gunmen posing as police officers. Police said they believe the intruders were looking for drug money, and that a third person was involved.
The boy was left unharmed Saturday night in a Las Vegas neighborhood, where a bus driver saw him and contacted authorities.
Police have said Cole's abduction was a message by Mexican methamphetamine dealers to Clemens Fred Tinnemeyer, the boy's grandfather, who police said disappeared after stealing millions of dollars in drug money.
Tinnemeyer, 51, was being held in federal custody in California after his arrest Friday in Riverside, Calif., on a material witness warrant issued by a federal court in Nevada.
A woman identified as Tinnemeyer's companion, Terri Leavy, 42, was also held as a material witness following her arrest Monday in Fontana, Calif.
Neither Leavy nor Tinnemeyer has been charged in the kidnapping case. Their attorney, Joan Politeo, declined to comment after a court hearing Monday.
Under federal law, Tinnemeyer and Leavy can be held for a "reasonable amount of time" until a deposition can be taken or they testify under oath.
Police Capt. Vincent Cannito has said authorities are still looking for Jesus Gastelum, a Mexican citizen in his mid-30s who also used the name Ferdinand Gastelum. Police have not said how Gastelum might be connected with the case.
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