Guzmán is now being held in isolation in another part of the prison, a Mexican security source said.
Manuel Merino, head of Mexico's extradition office, said that the Mexican government will send a diplomatic note to avoid the execution.
Ismael "El Mayo" Zambada jointly heads the powerful Sinaloa cartel and, with Guzmán facing possible extradition to the U.S., it falls to Zambada to maintain the gang's ranking as the world's largest.
The American actor expressed no regrets about his clandestine visit to interview the Mexican drug lord.
One senior official in the ruling Institutional Revolutionary Party said intelligence services got wind of Guzmán because they were tracking his henchman Iván Gastelum.
"The capture of Mr. Guzmán has been a high priority for both Mexico and the United States," White House spokesman Josh Earnest said at a news briefing.
His exploits in pulling off a clandestine interview with the world's most notorious drug kingpin shocked Hollywood.
Intelligence reports show that the Mexican actress met with Guzmán's lawyers four times.
As a U.S. citizen, the Mexican actress may have violated the restrictions of the OFAC under the Kingpin Act.
Guzmán's attorney Juan Pablo Badillo has said the defense has already filed six motions to challenge extradition requests.