Federal prosecutors in New York have announced plans to request Guzman's extradition for smuggling tonnes of narcotics, and several other US cities have indicted him on a slew of charges.
The 56-year-old Sinaloa cartel boss is already facing drug trafficking and organised crime charges, with a Mexican judge required to decide by today whether to put him on trial.
After 13 years on the run, the 56-year-old drug lord was captured by Mexican marines in a Pacific beach town on Saturday following a US-backed manhunt that involved a drone and cellphone taps.
Mexican officials have yet to say whether they would accept a US extradition request.
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Raul Benitez Manaut, a security expert at Mexico's National Autonomous University, said the injunction, known as an "amparo," is a tactic for "Guzman to stay in Mexico and delay the case."
An extradition can take a long time to take place because a suspect must first be convicted in Mexico, he said.
After a court convicts a suspect, Mexican authorities must then decide whether to extradite the convict immediately or make him serve his sentence in Mexico.