(CNN) -- Could the captured Sinaloa cartel boss who was one of Mexico's most wanted fugitives be heading to the United States for trial?
He will, if U.S. federal prosecutors have anything to say about it.
Drug lord 'El Chapo' no longer on the run
Bob Nardoza, a spokesman for the U.S. attorney's office for the Eastern District of New York, said Sunday that American authorities plan to seek the extradition of Joaquin "El Chapo" Guzman.
Authorities captured the notorious drug lord Saturday in the Mexican Pacific resort city of Mazatlan.
Notorious Mexican drug lord arrested
Cases are pending against him in New York and several other United States jurisdictions, and it's not clear which requests would take priority.
But just because the United States wants to extradite him doesn't mean Guzman will be heading north of the border any time soon.
"Mexico is going to want to prosecute him. They're going to want the first shot at him," CNN law enforcement analyst Tom Fuentes said Sunday. "The extradition to the U.S. could happen at a later date, but I doubt it. I think that the Mexicans are going to want him, and they're going to want to keep him in prison down there."
Guzman escaped from a high-security Mexican prison in 2001, reportedly hiding in a laundry basket. Throughout the years, he avoided being caught because of his enormous power to bribe corrupt local, state and federal Mexican officials.
His nickname, which means "Shorty," matches his 5-foot-6-inch frame.
From New York to Chicago, Texas to San Diego, Guzman and his lieutenants are named in indictments for marijuana, cocaine and heroin trafficking, as well as racketeering, money laundering, kidnapping and conspiracy to commit murder.
In Chicago, the city's crime commission named Guzman its Public Enemy No. 1 last year.
But more than anywhere else, Fuentes said, the "Public Enemy No. 1" designation is true for Guzman in Mexico.
"He's responsible for the deaths of thousands of people. He's considered one of the richest men in the world, and the Sinaloa cartel...is considered the most prolific drug-trafficking organization in the world," said Fuentes, former assistant director of the FBI's Office of International Operations.
When Guzman escaped from prison, he had served seven years of a 20-year, nine-month sentence.
Mexico's attorney general's office said there were eight warrants for Guzman's arrest there -- two tied to his 2001 escape, and six more for alleged crimes committed since then.
Authorities said they were taking him to the Altiplano prison outside Mexico City on Saturday, where he was set to be interrogated.
No attorney had yet come forward representing the cartel boss, officials said, and no extradition request had been made.
Eduardo Medina Mora, the Mexican ambassador to the United States, told The New York Times that authorities from the United States and Mexico had been working together on the case for months, but hadn't worked out whether Guzman would be extradited.
"I think it's important that first he faces the charges against him in Mexico," Medina Mora told the newspaper.
Rep. Michael McCaul, chairman of the House Homeland Security Committee, said Mexican officials should consider extradition now.
"The normal sequence is, Mexico being a sovereign nation, (it) has the first prosecution. However, there's a history here. He escaped from a prison in 2001. There is corruption in that country. And I would ask that the Mexicans consider extraditing him to the United States, where he will be put into a 'supermax' prison under tight security, where he cannot escape, and be brought to justice with a life sentence," McCaul told ABC's "This Week."
"I think that would be the best course of action for not only Mexico, but also the United States, in ensuring that what happened in 2001 does not happen again."
How likely extradition is, the Texas Republican congressm
an said, depends on how much pressure the State Department puts on Mexico's government. But he said it would be worth the effort.
"The track record's not good with this individual," he said. "This is an exceptional case. This is the largest, biggest drug lord we've ever seen in the world."
Phil Jordan, who spent three decades with the DEA and headed the agency's El Paso Intelligence Center, said extraditing Guzman is the only way to truly cripple his organization.
"It is a significant arrest, provided he gets extradited immediately to the United States," Jordan told CNN Saturday. "If he does not get extradited, then he will be allowed to escape within a period of time. ... If he is, in fact, incarcerated, until he gets extradited to the United States, it will be business as usual."