Guzman, who has been called Mexico's Osama bin Laden, was captured last week after eluding police for 13 years.
Mexican authorities arrested him after receiving intelligence from U.S. immigration and drug enforcement agents.
He is allegedly responsible for 25 percent of drugs entering the United States.
McCaul said on ABC's "This Week" that the arrest was a significant victory for both Mexico and the United States.
"There's a history here. He escaped from a prison in 2001. There is corruption in that country," he said. "And I would ask that the Mexicans consider extraditing him to the United States where he will be put in a supermax prison under tight security where he cannot escape and be brought to justice with a life imprisonment sentence."
Multiple indictments in multiple cities, including New York and Chicago, have been filed against Guzman, McCaul noted.
"We could deal with him in a secure, safe way and bring him to justice," he said.